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+ cornerNotchRadius * sin(225)"] ] } ], "lattice": { "a": ["2 * circumradius", "0"], "b": ["0", "2 * circumradius"] } } ,"eight-star-squares-khargird":{ "schema": 1, "id": "eight-star-squares-khargird", "name": "Eight-point star and square checkerboard", "category": "ceramic", "parameters": { "edge": {"value": 40, "min": 10, "max": 150, "label": "Small square side"}, "unitLength": {"expr": "edge * (2 + sqrt(2))"} }, "tiles": [ { "polygon": [ ["0", "unitLength * (-2 + sqrt(2)) / 2"], ["unitLength * (3 - 2 * sqrt(2)) / 2", "unitLength * (1 - sqrt(2)) / 2"], ["unitLength * (-1 + sqrt(2)) / 2", "unitLength * (1 - sqrt(2)) / 2"], ["unitLength * (-1 + sqrt(2)) / 2", "unitLength * (-3 + 2 * sqrt(2)) / 2"], ["unitLength * (2 - sqrt(2)) / 2", "0"], ["unitLength * (-1 + sqrt(2)) / 2", "unitLength * (3 - 2 * sqrt(2)) / 2"], ["unitLength * (-1 + sqrt(2)) / 2", "unitLength * (-1 + sqrt(2)) / 2"], ["unitLength * (3 - 2 * sqrt(2)) / 2", "unitLength * (-1 + sqrt(2)) / 2"], ["0", "unitLength * (2 - sqrt(2)) / 2"], ["unitLength * (-3 + 2 * sqrt(2)) / 2", "unitLength * (-1 + sqrt(2)) / 2"], ["unitLength * (1 - sqrt(2)) / 2", "unitLength * (-1 + sqrt(2)) / 2"], ["unitLength * (1 - sqrt(2)) / 2", "unitLength * (3 - 2 * sqrt(2)) / 2"], ["unitLength * (-2 + sqrt(2)) / 2", "0"], ["unitLength * (1 - sqrt(2)) / 2", "unitLength * (-3 + 2 * sqrt(2)) / 2"], ["unitLength * (1 - sqrt(2)) / 2", "unitLength * (1 - sqrt(2)) / 2"], ["unitLength * (-3 + 2 * sqrt(2)) / 2", "unitLength * (1 - sqrt(2)) / 2"] ] }, { "polygon": [ ["unitLength * (3 - 2 * sqrt(2)) / 2", "unitLength * (-1 + sqrt(2)) / 2"], ["unitLength * (-1 + sqrt(2)) / 2", "unitLength * (-1 + sqrt(2)) / 2"], ["unitLength * (-1 + sqrt(2)) / 2", "unitLength / 2"], ["0", "unitLength * (2 - sqrt(2)) / 2"] ] }, { "polygon": [ ["unitLength * (-1 + 2 * sqrt(2)) / 2", "unitLength * (-3 + sqrt(2)) / 2"], ["unitLength", "unitLength * -sqrt(2) / 2"], ["unitLength * (3 - sqrt(2)) / 2", "-unitLength / 2"], ["unitLength * (3 - sqrt(2)) / 2", "unitLength * (-3 + sqrt(2)) / 2"] ] }, { "polygon": [ ["unitLength * (-1 + 2 * sqrt(2)) / 2", "unitLength * (3 - sqrt(2)) / 2"], ["unitLength * (3 - sqrt(2)) / 2", "unitLength * (3 - sqrt(2)) / 2"], ["unitLength * (3 - sqrt(2)) / 2", "unitLength / 2"], ["unitLength", "unitLength * sqrt(2) / 2"] ] }, { "polygon": [ ["unitLength * (3 - 2 * sqrt(2)) / 2", "unitLength * (1 - sqrt(2)) / 2"], ["0", "unitLength * (-2 + sqrt(2)) / 2"], ["unitLength * (-1 + sqrt(2)) / 2", "-unitLength / 2"], ["unitLength * (-1 + sqrt(2)) / 2", "unitLength * (1 - sqrt(2)) / 2"] ] }, { "polygon": [ ["unitLength", "unitLength * -sqrt(2) / 2"], ["unitLength * (1 + sqrt(2)) / 2", "-unitLength / 2"], ["unitLength", "unitLength * (-2 + sqrt(2)) / 2"], ["unitLength * (3 - sqrt(2)) / 2", "-unitLength / 2"] ] }, { "polygon": [ ["unitLength * (-1 + sqrt(2)) / 2", "unitLength / 2"], ["unitLength / 2", "unitLength / 2"], ["unitLength / 2", "unitLength * (-1 + sqrt(2)) / 2"], ["unitLength * (-1 + sqrt(2)) / 2", "unitLength * (-1 + sqrt(2)) / 2"] ] }, { "polygon": [ ["unitLength * (-1 + sqrt(2)) / 2", "unitLength * (3 - 2 * sqrt(2)) / 2"], ["unitLength * (2 - sqrt(2)) / 2", "0"], ["unitLength / 2", "unitLength * (-1 + sqrt(2)) / 2"], ["unitLength * (-1 + sqrt(2)) / 2", "unitLength * (-1 + sqrt(2)) / 2"] ] }, { "polygon": [ ["unitLength * (-1 + sqrt(2)) / 2", "unitLength * (-3 + 2 * sqrt(2)) / 2"], ["unitLength * (-1 + sqrt(2)) / 2", "unitLength * (1 - sqrt(2)) / 2"], ["unitLength / 2", "unitLength * (1 - sqrt(2)) / 2"], ["unitLength * (2 - sqrt(2)) / 2", "0"] ] }, { "polygon": [ ["unitLength * (-1 + sqrt(2)) / 2", "unitLength * (1 - sqrt(2)) / 2"], ["unitLength / 2", "unitLength * (1 - sqrt(2)) / 2"], ["unitLength / 2", "-unitLength / 2"], ["unitLength * (-1 + sqrt(2)) / 2", "-unitLength / 2"] ] }, { "polygon": [ ["unitLength * (3 - sqrt(2)) / 2", "unitLength * (-3 + sqrt(2)) / 2"], ["unitLength / 2", "unitLength * (-3 + sqrt(2)) / 2"], ["unitLength * sqrt(2) / 2", "-unitLength"], ["unitLength * (3 - sqrt(2)) / 2", "unitLength * (1 - 2 * sqrt(2)) / 2"] ] }, { "polygon": [ ["unitLength / 2", "-unitLength / 2"], ["unitLength * (3 - sqrt(2)) / 2", "-unitLength / 2"], ["unitLength * (3 - sqrt(2)) / 2", "unitLength * (-3 + sqrt(2)) / 2"], ["unitLength / 2", "unitLength * (-3 + sqrt(2)) / 2"] ] }, { "polygon": [ ["unitLength * (3 - sqrt(2)) / 2", "unitLength * (-1 + 2 * sqrt(2)) / 2"], ["unitLength * sqrt(2) / 2", "unitLength"], ["unitLength / 2", "unitLength * (3 - sqrt(2)) / 2"], ["unitLength * (3 - sqrt(2)) / 2", "unitLength * (3 - sqrt(2)) / 2"] ] }, { "polygon": [ ["unitLength / 2", "unitLength * (3 - sqrt(2)) / 2"], ["unitLength * (3 - sqrt(2)) / 2", "unitLength * (3 - sqrt(2)) / 2"], ["unitLength * (3 - sqrt(2)) / 2", "unitLength / 2"], ["unitLength / 2", "unitLength / 2"] ] }, { "polygon": [ ["unitLength", "unitLength * sqrt(2) / 2"], ["unitLength * (3 - sqrt(2)) / 2", "unitLength / 2"], ["unitLength", "unitLength * (2 - sqrt(2)) / 2"], ["unitLength * (1 + sqrt(2)) / 2", "unitLength / 2"] ] }, { "polygon": [ ["unitLength * (2 - sqrt(2)) / 2", "0"], ["unitLength / 2", "unitLength * (1 - sqrt(2)) / 2"], ["unitLength * sqrt(2) / 2", "0"], ["unitLength / 2", "unitLength * (-1 + sqrt(2)) / 2"] ] }, { "polygon": [ ["unitLength * (2 + sqrt(2)) / 2", "0"], ["unitLength * 3 / 2", "unitLength * (-1 + sqrt(2)) / 2"], ["unitLength * (4 - sqrt(2)) / 2", "0"], ["unitLength * 3 / 2", "unitLength * (1 - sqrt(2)) / 2"] ] }, { "polygon": [ ["unitLength * (1 + sqrt(2)) / 2", "-unitLength / 2"], ["unitLength * 3 / 2", "-unitLength / 2"], ["unitLength * (4 - sqrt(2)) / 2", "unitLength * (-2 + sqrt(2)) / 2"], ["unitLength", "unitLength * (-2 + sqrt(2)) / 2"] ] }, { "polygon": [ ["unitLength * (3 - sqrt(2)) / 2", "-unitLength / 2"], ["unitLength", "unitLength * (-2 + sqrt(2)) / 2"], ["unitLength * sqrt(2) / 2", "unitLength * (-2 + sqrt(2)) / 2"], ["unitLength / 2", "-unitLength / 2"] ] }, { "polygon": [ ["unitLength * (3 - sqrt(2)) / 2", "unitLength / 2"], ["unitLength / 2", "unitLength / 2"], ["unitLength * sqrt(2) / 2", "unitLength * (2 - sqrt(2)) / 2"], ["unitLength", "unitLength * (2 - sqrt(2)) / 2"] ] }, { "polygon": [ ["unitLength * (1 + sqrt(2)) / 2", "unitLength / 2"], ["unitLength", "unitLength * (2 - sqrt(2)) / 2"], ["unitLength * (4 - sqrt(2)) / 2", "unitLength * (2 - sqrt(2)) / 2"], ["unitLength * 3 / 2", "unitLength / 2"] ] }, { "polygon": [ ["unitLength * (4 - sqrt(2)) / 2", "unitLength * (-2 + sqrt(2)) / 2"], ["unitLength * (4 - sqrt(2)) / 2", "unitLength * (2 - sqrt(2)) / 2"], ["unitLength * sqrt(2) / 2", "unitLength * (2 - sqrt(2)) / 2"], ["unitLength * sqrt(2) / 2", "unitLength * (-2 + sqrt(2)) / 2"] ] }, { "polygon": [ ["unitLength * (4 - sqrt(2)) / 2", "unitLength * (-2 + sqrt(2)) / 2"], ["unitLength * 3 / 2", "-unitLength / 2"], ["unitLength * 3 / 2", "unitLength * (1 - sqrt(2)) / 2"], ["unitLength * (4 - sqrt(2)) / 2", "0"] ] }, { "polygon": [ ["unitLength * sqrt(2) / 2", "unitLength * (-2 + sqrt(2)) / 2"], ["unitLength * sqrt(2) / 2", "0"], ["unitLength / 2", "unitLength * (1 - sqrt(2)) / 2"], ["unitLength / 2", "-unitLength / 2"] ] }, { "polygon": [ ["unitLength * 3 / 2", "unitLength / 2"], ["unitLength * (4 - sqrt(2)) / 2", "unitLength * (2 - sqrt(2)) / 2"], ["unitLength * (4 - sqrt(2)) / 2", "0"], ["unitLength * 3 / 2", "unitLength * (-1 + sqrt(2)) / 2"] ] }, { "polygon": [ ["unitLength / 2", "unitLength / 2"], ["unitLength / 2", "unitLength * (-1 + sqrt(2)) / 2"], ["unitLength * sqrt(2) / 2", "0"], ["unitLength * sqrt(2) / 2", "unitLength * (2 - sqrt(2)) / 2"] ] } ], "lattice": { "a": ["unitLength", "unitLength"], "b": ["unitLength", "-unitLength"] } } ,"eight-star-twelve-star-kite":{ "schema": 1, "id": "eight-star-twelve-star-kite", "name": "Eight- and twelve-point stars with kites", "category": "ceramic", "parameters": { "edge": { "value": 30, "min": 10, "max": 100, "label": "Star edge" } }, "tiles": [ { "polygon": [ ["(-sqrt(2) - sqrt(6)) * edge / 2", "(-sqrt(2) - sqrt(6)) * edge / 2"], ["(-sqrt(2) - sqrt(6)) * edge / 4", "(-3 * sqrt(2) - sqrt(6)) * edge / 4"], ["-sqrt(2) * edge / 2", "(-2 * sqrt(2) - sqrt(6)) * edge / 2"], ["0", "(-sqrt(2) - sqrt(6)) * edge / 2"], ["sqrt(2) * edge / 2", "(-2 * sqrt(2) - sqrt(6)) * edge / 2"], ["(sqrt(2) + sqrt(6)) * edge / 4", "(-3 * sqrt(2) - sqrt(6)) * edge / 4"], ["(sqrt(2) + sqrt(6)) * edge / 2", "(-sqrt(2) - sqrt(6)) * edge / 2"], ["(3 * sqrt(2) + sqrt(6)) * edge / 4", "(-sqrt(2) - sqrt(6)) * edge / 4"], ["(2 * sqrt(2) + sqrt(6)) * edge / 2", "-sqrt(2) * edge / 2"], ["(sqrt(2) + sqrt(6)) * edge / 2", "0"], ["(2 * sqrt(2) + sqrt(6)) * edge / 2", "sqrt(2) * edge / 2"], ["(3 * sqrt(2) + sqrt(6)) * edge / 4", "(sqrt(2) + sqrt(6)) * edge / 4"], ["(sqrt(2) + sqrt(6)) * edge / 2", "(sqrt(2) + sqrt(6)) * edge / 2"], ["(sqrt(2) + sqrt(6)) * edge / 4", "(3 * sqrt(2) + sqrt(6)) * edge / 4"], ["sqrt(2) * edge / 2", "(2 * sqrt(2) + sqrt(6)) * edge / 2"], ["0", "(sqrt(2) + sqrt(6)) * edge / 2"], ["-sqrt(2) * edge / 2", "(2 * sqrt(2) + sqrt(6)) * edge / 2"], ["(-sqrt(2) - sqrt(6)) * edge / 4", "(3 * sqrt(2) + sqrt(6)) * edge / 4"], ["(-sqrt(2) - sqrt(6)) * edge / 2", "(sqrt(2) + sqrt(6)) * edge / 2"], ["(-3 * sqrt(2) - sqrt(6)) * edge / 4", "(sqrt(2) + sqrt(6)) * edge / 4"], ["(-2 * sqrt(2) - sqrt(6)) * edge / 2", "sqrt(2) * edge / 2"], ["(-sqrt(2) - sqrt(6)) * edge / 2", "0"], ["(-2 * sqrt(2) - sqrt(6)) * edge / 2", "-sqrt(2) * edge / 2"], ["(-3 * sqrt(2) - sqrt(6)) * edge / 4", "(-sqrt(2) - sqrt(6)) * edge / 4"] ] }, { "polygon": [ ["(2 * sqrt(2) + sqrt(6)) * edge / 2", "sqrt(2) * edge / 2"], ["(2 * sqrt(2) + sqrt(6)) * edge", "0"], ["(1 + 4 * sqrt(2) + sqrt(3) + 2 * sqrt(6)) * edge / 2", "(-1 + sqrt(3)) * edge / 2"], ["(1 + 4 * sqrt(2) + sqrt(3) + 2 * sqrt(6)) * edge / 2", "(-1 + 2 * sqrt(2) + sqrt(3)) * edge / 2"], ["(1 + 3 * sqrt(2) + sqrt(3) + 2 * sqrt(6)) * edge / 2", "(-1 + 2 * sqrt(2) + sqrt(3) + sqrt(6)) * edge / 2"], ["(3 * sqrt(2) + 2 * sqrt(6)) * edge / 2", "(2 * sqrt(2) + sqrt(6)) * edge / 2"] ] }, { "polygon": [ ["sqrt(2) * edge / 2", "(2 * sqrt(2) + sqrt(6)) * edge / 2"], ["(2 * sqrt(2) + sqrt(6)) * edge / 2", "(3 * sqrt(2) + 2 * sqrt(6)) * edge / 2"], ["(-1 + 2 * sqrt(2) + sqrt(3) + sqrt(6)) * edge / 2", "(1 + 3 * sqrt(2) + sqrt(3) + 2 * sqrt(6)) * edge / 2"], ["(-1 + 2 * sqrt(2) + sqrt(3)) * edge / 2", "(1 + 4 * sqrt(2) + sqrt(3) + 2 * sqrt(6)) * edge / 2"], ["(-1 + sqrt(3)) * edge / 2", "(1 + 4 * sqrt(2) + sqrt(3) + 2 * sqrt(6)) * edge / 2"], ["0", "(2 * sqrt(2) + sqrt(6)) * edge"] ] }, { "polygon": [ ["(-2 * sqrt(2) - sqrt(6)) * edge / 2", "-sqrt(2) * edge / 2"], ["(-2 * sqrt(2) - sqrt(6)) * edge", "0"], ["(-1 - 4 * sqrt(2) - sqrt(3) - 2 * sqrt(6)) * edge / 2", "(1 - sqrt(3)) * edge / 2"], ["(-1 - 4 * sqrt(2) - sqrt(3) - 2 * sqrt(6)) * edge / 2", "(1 - 2 * sqrt(2) - sqrt(3)) * edge / 2"], ["(-1 - 3 * sqrt(2) - sqrt(3) - 2 * sqrt(6)) * edge / 2", "(1 - 2 * sqrt(2) - sqrt(3) - sqrt(6)) * edge / 2"], ["(-3 * sqrt(2) - 2 * sqrt(6)) * edge / 2", "(-2 * sqrt(2) - sqrt(6)) * edge / 2"] ] }, { "polygon": [ ["-sqrt(2) * edge / 2", "(-2 * sqrt(2) - sqrt(6)) * edge / 2"], ["(-2 * sqrt(2) - sqrt(6)) * edge / 2", "(-3 * sqrt(2) - 2 * sqrt(6)) * edge / 2"], ["(1 - 2 * sqrt(2) - sqrt(3) - sqrt(6)) * edge / 2", "(-1 - 3 * sqrt(2) - sqrt(3) - 2 * sqrt(6)) * edge / 2"], ["(1 - 2 * sqrt(2) - sqrt(3)) * edge / 2", "(-1 - 4 * sqrt(2) - sqrt(3) - 2 * sqrt(6)) * edge / 2"], ["(1 - sqrt(3)) * edge / 2", "(-1 - 4 * sqrt(2) - sqrt(3) - 2 * sqrt(6)) * edge / 2"], ["0", "(-2 * sqrt(2) - sqrt(6)) * edge"] ] }, { "polygon": [ ["(sqrt(2) + sqrt(6)) * edge / 2", "(sqrt(2) + sqrt(6)) * edge / 2"], ["(3 * sqrt(2) + 2 * sqrt(6)) * edge / 2", "(2 * sqrt(2) + sqrt(6)) * edge / 2"], ["(2 + 3 * sqrt(2) + 2 * sqrt(6)) * edge / 2", "(2 + 2 * sqrt(2) + sqrt(6)) * edge / 2"], ["(1 + sqrt(2) + sqrt(6)) * edge", "(1 + sqrt(2) + sqrt(6)) * edge"], ["(2 + 2 * sqrt(2) + sqrt(6)) * edge / 2", "(2 + 3 * sqrt(2) + 2 * sqrt(6)) * edge / 2"], ["(2 * sqrt(2) + sqrt(6)) * edge / 2", "(3 * sqrt(2) + 2 * sqrt(6)) * edge / 2"] ] }, { "polygon": [ ["(-sqrt(2) - sqrt(6)) * edge / 2", "(-sqrt(2) - sqrt(6)) * edge / 2"], ["(-3 * sqrt(2) - 2 * sqrt(6)) * edge / 2", "(-2 * sqrt(2) - sqrt(6)) * edge / 2"], ["(-2 - 3 * sqrt(2) - 2 * sqrt(6)) * edge / 2", "(-2 - 2 * sqrt(2) - sqrt(6)) * edge / 2"], ["(-1 - sqrt(2) - sqrt(6)) * edge", "(-1 - sqrt(2) - sqrt(6)) * edge"], ["(-2 - 2 * sqrt(2) - sqrt(6)) * edge / 2", "(-2 - 3 * sqrt(2) - 2 * sqrt(6)) * edge / 2"], ["(-2 * sqrt(2) - sqrt(6)) * edge / 2", "(-3 * sqrt(2) - 2 * sqrt(6)) * edge / 2"] ] }, { "polygon": [ ["sqrt(2) * edge / 2", "(-2 * sqrt(2) - sqrt(6)) * edge / 2"], ["0", "(-2 * sqrt(2) - sqrt(6)) * edge"], ["(-1 + sqrt(3)) * edge / 2", "(-1 - 4 * sqrt(2) - sqrt(3) - 2 * sqrt(6)) * edge / 2"], ["(-1 + 2 * sqrt(2) + sqrt(3)) * edge / 2", "(-1 - 4 * sqrt(2) - sqrt(3) - 2 * sqrt(6)) * edge / 2"], ["(-1 + 2 * sqrt(2) + sqrt(3) + sqrt(6)) * edge / 2", "(-1 - 3 * sqrt(2) - sqrt(3) - 2 * sqrt(6)) * edge / 2"], ["(2 * sqrt(2) + sqrt(6)) * edge / 2", "(-3 * sqrt(2) - 2 * sqrt(6)) * edge / 2"] ] }, { "polygon": [ ["(2 * sqrt(2) + sqrt(6)) * edge / 2", "-sqrt(2) * edge / 2"], ["(3 * sqrt(2) + 2 * sqrt(6)) * edge / 2", "(-2 * sqrt(2) - sqrt(6)) * edge / 2"], ["(1 + 3 * sqrt(2) + sqrt(3) + 2 * sqrt(6)) * edge / 2", "(1 - 2 * sqrt(2) - sqrt(3) - sqrt(6)) * edge / 2"], ["(1 + 4 * sqrt(2) + sqrt(3) + 2 * sqrt(6)) * edge / 2", "(1 - 2 * sqrt(2) - sqrt(3)) * edge / 2"], ["(1 + 4 * sqrt(2) + sqrt(3) + 2 * sqrt(6)) * edge / 2", "(1 - sqrt(3)) * edge / 2"], ["(2 * sqrt(2) + sqrt(6)) * edge", "0"] ] }, { "polygon": [ ["-sqrt(2) * edge / 2", "(2 * sqrt(2) + sqrt(6)) * edge / 2"], ["0", "(2 * sqrt(2) + sqrt(6)) * edge"], ["(1 - sqrt(3)) * edge / 2", "(1 + 4 * sqrt(2) + sqrt(3) + 2 * sqrt(6)) * edge / 2"], ["(1 - 2 * sqrt(2) - sqrt(3)) * edge / 2", "(1 + 4 * sqrt(2) + sqrt(3) + 2 * sqrt(6)) * edge / 2"], ["(1 - 2 * sqrt(2) - sqrt(3) - sqrt(6)) * edge / 2", "(1 + 3 * sqrt(2) + sqrt(3) + 2 * sqrt(6)) * edge / 2"], ["(-2 * sqrt(2) - sqrt(6)) * edge / 2", "(3 * sqrt(2) + 2 * sqrt(6)) * edge / 2"] ] }, { "polygon": [ ["(-2 * sqrt(2) - sqrt(6)) * edge / 2", "sqrt(2) * edge / 2"], ["(-3 * sqrt(2) - 2 * sqrt(6)) * edge / 2", "(2 * sqrt(2) + sqrt(6)) * edge / 2"], ["(-1 - 3 * sqrt(2) - sqrt(3) - 2 * sqrt(6)) * edge / 2", "(-1 + 2 * sqrt(2) + sqrt(3) + sqrt(6)) * edge / 2"], ["(-1 - 4 * sqrt(2) - sqrt(3) - 2 * sqrt(6)) * edge / 2", "(-1 + 2 * sqrt(2) + sqrt(3)) * edge / 2"], ["(-1 - 4 * sqrt(2) - sqrt(3) - 2 * sqrt(6)) * edge / 2", "(-1 + sqrt(3)) * edge / 2"], ["(-2 * sqrt(2) - sqrt(6)) * edge", "0"] ] }, { "polygon": [ ["(-sqrt(2) - sqrt(6)) * edge / 2", "(sqrt(2) + sqrt(6)) * edge / 2"], ["(-2 * sqrt(2) - sqrt(6)) * edge / 2", "(3 * sqrt(2) + 2 * sqrt(6)) * edge / 2"], ["(-2 - 2 * sqrt(2) - sqrt(6)) * edge / 2", "(2 + 3 * sqrt(2) + 2 * sqrt(6)) * edge / 2"], ["(-1 - sqrt(2) - sqrt(6)) * edge", "(1 + sqrt(2) + sqrt(6)) * edge"], ["(-2 - 3 * sqrt(2) - 2 * sqrt(6)) * edge / 2", "(2 + 2 * sqrt(2) + sqrt(6)) * edge / 2"], ["(-3 * sqrt(2) - 2 * 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edge / 2"], ["edge / 2", "sqrt(3) * edge / 2"], ["0", "2 * sqrt(3) * edge / 2"], ["-edge / 2", "sqrt(3) * edge / 2"], ["-3 * edge / 2", "sqrt(3) * edge / 2"], ["-2 * edge / 2", "0"] ] }, { "polygon": [ ["4 * edge / 2", "2 * sqrt(3) * edge / 2"], ["5 * edge / 2", "3 * sqrt(3) * edge / 2"], ["4 * edge / 2", "4 * sqrt(3) * edge / 2"], ["2 * edge / 2", "4 * sqrt(3) * edge / 2"], ["edge / 2", "3 * sqrt(3) * edge / 2"], ["2 * edge / 2", "2 * sqrt(3) * edge / 2"] ] }, { "polygon": [ ["6 * edge / 2", "0"], ["5 * edge / 2", "sqrt(3) * edge / 2"], ["3 * edge / 2", "sqrt(3) * edge / 2"], ["2 * edge / 2", "0"], ["3 * edge / 2", "-sqrt(3) * edge / 2"], ["5 * edge / 2", "-sqrt(3) * edge / 2"] ] }, { "polygon": [ ["8 * edge / 2", "0"], ["9 * edge / 2", "-sqrt(3) * edge / 2"], ["11 * edge / 2", "-sqrt(3) * edge / 2"], ["12 * edge / 2", "0"], ["11 * edge / 2", "sqrt(3) * edge / 2"], ["9 * edge / 2", "sqrt(3) * edge / 2"] ] }, { "polygon": [ ["10 * edge / 2", "4 * sqrt(3) * edge / 2"], ["9 * edge / 2", "3 * sqrt(3) * edge / 2"], ["10 * edge / 2", "2 * sqrt(3) * edge / 2"], ["12 * edge / 2", "2 * sqrt(3) * edge / 2"], ["13 * edge / 2", "3 * sqrt(3) * edge / 2"], ["12 * edge / 2", "4 * sqrt(3) * edge / 2"] ] }, { "polygon": [ ["4 * edge / 2", "2 * sqrt(3) * edge / 2"], ["2 * edge / 2", "2 * sqrt(3) * edge / 2"], ["edge / 2", "3 * sqrt(3) * edge / 2"], ["0", "2 * sqrt(3) * edge / 2"], ["edge / 2", "sqrt(3) * edge / 2"], ["3 * edge / 2", "sqrt(3) * edge / 2"] ] }, { "polygon": [ ["4 * edge / 2", "4 * sqrt(3) * edge / 2"], ["3 * edge / 2", "5 * sqrt(3) * edge / 2"], ["edge / 2", "5 * sqrt(3) * edge / 2"], ["0", "4 * sqrt(3) * edge / 2"], ["edge / 2", "3 * sqrt(3) * edge / 2"], ["2 * edge / 2", "4 * sqrt(3) * edge / 2"] ] }, { "polygon": [ ["7 * edge / 2", "sqrt(3) * edge / 2"], ["6 * edge / 2", "2 * sqrt(3) * edge / 2"], ["4 * edge / 2", "2 * sqrt(3) * edge / 2"], ["3 * edge / 2", "sqrt(3) * edge / 2"], ["5 * edge / 2", "sqrt(3) * edge / 2"], ["6 * edge / 2", "0"] ] }, { "polygon": [ ["6 * edge / 2", "6 * sqrt(3) * edge / 2"], ["5 * edge / 2", "5 * sqrt(3) * edge / 2"], ["3 * edge / 2", "5 * sqrt(3) * edge / 2"], ["4 * edge / 2", "4 * sqrt(3) * edge / 2"], ["6 * edge / 2", "4 * sqrt(3) * edge / 2"], ["7 * edge / 2", "5 * sqrt(3) * edge / 2"] ] }, { "polygon": [ ["7 * edge / 2", "sqrt(3) * edge / 2"], ["8 * edge / 2", "0"], ["9 * edge / 2", "sqrt(3) * edge / 2"], ["11 * edge / 2", "sqrt(3) * edge / 2"], ["10 * edge / 2", "2 * sqrt(3) * edge / 2"], ["8 * edge / 2", "2 * sqrt(3) * edge / 2"] ] }, { "polygon": [ ["8 * edge / 2", "6 * sqrt(3) * edge / 2"], ["7 * edge / 2", "5 * sqrt(3) * edge / 2"], ["8 * edge / 2", "4 * sqrt(3) * edge / 2"], ["10 * edge / 2", "4 * sqrt(3) * edge / 2"], ["11 * edge / 2", "5 * sqrt(3) * edge / 2"], ["9 * edge / 2", "5 * sqrt(3) * edge / 2"] ] }, { "polygon": [ ["10 * edge / 2", "2 * sqrt(3) * edge / 2"], ["11 * edge / 2", "sqrt(3) * edge / 2"], ["13 * edge / 2", "sqrt(3) * edge / 2"], ["14 * edge / 2", "2 * sqrt(3) * edge / 2"], ["13 * edge / 2", "3 * sqrt(3) * edge / 2"], ["12 * edge / 2", "2 * sqrt(3) * edge / 2"] ] }, { "polygon": [ ["10 * edge / 2", "4 * sqrt(3) * edge / 2"], ["12 * edge / 2", "4 * sqrt(3) * edge / 2"], ["13 * edge / 2", "3 * sqrt(3) * edge / 2"], ["14 * edge / 2", "4 * sqrt(3) * edge / 2"], ["13 * edge / 2", "5 * sqrt(3) * edge / 2"], ["11 * edge / 2", "5 * sqrt(3) * edge / 2"] ] }, { "polygon": [ ["edge / 2", "3 * sqrt(3) * edge / 2"], ["0", "4 * sqrt(3) * edge / 2"], ["-edge / 2", "3 * sqrt(3) * edge / 2"], ["0", "2 * sqrt(3) * edge / 2"] ] }, { "polygon": [ ["6 * edge / 2", "2 * sqrt(3) * edge / 2"], ["7 * edge / 2", "3 * sqrt(3) * edge / 2"], ["5 * edge / 2", "3 * sqrt(3) * edge / 2"], ["4 * edge / 2", "2 * sqrt(3) * edge / 2"] ] }, { "polygon": [ ["6 * edge / 2", "4 * sqrt(3) * edge / 2"], ["4 * edge / 2", "4 * sqrt(3) * edge / 2"], ["5 * edge / 2", "3 * sqrt(3) * edge / 2"], ["7 * edge / 2", "3 * sqrt(3) * edge / 2"] ] }, { "polygon": [ ["7 * edge / 2", "-sqrt(3) * edge / 2"], ["8 * edge / 2", "0"], ["7 * edge / 2", "sqrt(3) * edge / 2"], ["6 * edge / 2", "0"] ] }, { "polygon": [ ["7 * edge / 2", "sqrt(3) * edge / 2"], ["8 * edge / 2", "2 * sqrt(3) * edge / 2"], ["7 * edge / 2", "3 * sqrt(3) * edge / 2"], ["6 * edge / 2", "2 * sqrt(3) * edge / 2"] ] }, { "polygon": [ ["7 * edge / 2", "5 * sqrt(3) * edge / 2"], ["6 * edge / 2", "4 * sqrt(3) * edge / 2"], ["7 * edge / 2", "3 * sqrt(3) * edge / 2"], ["8 * edge / 2", "4 * sqrt(3) * edge / 2"] ] }, { "polygon": [ ["8 * edge / 2", "2 * sqrt(3) * edge / 2"], ["10 * edge / 2", "2 * sqrt(3) * edge / 2"], ["9 * edge / 2", "3 * sqrt(3) * edge / 2"], ["7 * edge / 2", "3 * sqrt(3) * edge / 2"] ] }, { "polygon": [ ["8 * edge / 2", "4 * sqrt(3) * edge / 2"], ["7 * edge / 2", "3 * sqrt(3) * edge / 2"], ["9 * edge / 2", "3 * sqrt(3) * edge / 2"], ["10 * edge / 2", "4 * sqrt(3) * edge / 2"] ] } ], "lattice": { "a": ["7 * edge", "0"], "b": ["0", "3 * sqrt(3) * edge"] } } ,"hexagon-weave":{ "schema": 1, "id": "hexagon-weave", "name": "Hexagon weave", "category": "wood", "parameters": { "edge": { "value": 200, "min": 20, "max": 900, "label": "Hexagon side" }, "flat": { "expr": "sqrt(3) * edge / 2" } }, "tiles": [ { "polygon": [ ["flat", "edge / 2"], ["0", "edge"], ["-flat", "edge / 2"], ["-flat", "-edge / 2"], ["0", "-edge"], ["flat", "-edge / 2"] ] }, { "polygon": [ ["-2 * flat", "0"], ["0", "edge"], ["-flat", "3 * edge / 2"], ["-3 * flat", "edge / 2"] ] }, { "polygon": [ ["-flat", "3 * edge / 2"], ["flat", "edge / 2"], ["flat", "3 * edge / 2"], ["-flat", "5 * edge / 2"] ] }, { "polygon": [ ["flat", "-edge / 2"], ["2 * flat", "0"], ["2 * flat", "2 * edge"], ["flat", "3 * edge / 2"] ] } ], "lattice": { "a": ["3 * flat", "3 * edge / 2"], "b": ["3 * flat", "-3 * edge / 2"] } } ,"hexagon":{ "schema": 1, "id": "hexagon", "name": "Hexagon", "category": "ceramic", "parameters": { "edge": { "value": 100, "min": 10, "max": 1000, "label": "Side" } }, "tiles": [ { "polygon": [ ["edge", "0"], ["edge / 2", "sqrt(3) * edge / 2"], ["-edge / 2", "sqrt(3) * edge / 2"], ["-edge", "0"], ["-edge / 2", "-sqrt(3) * edge / 2"], ["edge / 2", "-sqrt(3) * edge / 2"] ] } ], "lattice": { "a": ["3 * edge / 2", "sqrt(3) * edge / 2"], "b": ["0", "sqrt(3) * edge"] } } ,"hexagram-dodecagon":{ "schema": 1, "id": "hexagram-dodecagon", "name": "Hexagram and dodecagon", "category": "ceramic", "parameters": { "edge": {"value": 50, "min": 10, "max": 500, "label": "Edge"}, "starDepthRatio": { "expr": "0.666667" }, "rootThree": {"expr": "sqrt(3)"} }, "tiles": [ { "polygon": [ ["edge * (2 + rootThree) / 2", "edge / 2"], ["edge * (3 + rootThree) / 2 + starDepthRatio * (edge * (3 + 2 * rootThree) / 4 - (edge * (3 + rootThree) / 2))", "edge * (1 + rootThree) / 2 + starDepthRatio * (edge * (2 + rootThree) / 4 - (edge * (1 + rootThree) / 2))"], ["edge * (1 + rootThree) / 2", "edge * (1 + rootThree) / 2"], ["edge / 2", "edge * (2 + rootThree) / 2"], ["0", "edge * (1 + rootThree) + starDepthRatio * (edge * (2 + rootThree) / 2 - (edge * (1 + rootThree)))"], ["-edge / 2", "edge * (2 + rootThree) / 2"], ["edge * (-1 - rootThree) / 2", "edge * (1 + rootThree) / 2"], ["edge * (-3 - rootThree) / 2 + starDepthRatio * (edge * (-3 - 2 * rootThree) / 4 - (edge * (-3 - rootThree) / 2))", "edge * (1 + rootThree) / 2 + starDepthRatio * (edge * (2 + rootThree) / 4 - (edge * (1 + rootThree) / 2))"], ["edge * (-2 - rootThree) / 2", "edge / 2"], ["edge * (-2 - rootThree) / 2", "-edge / 2"], ["edge * (-3 - rootThree) / 2 + starDepthRatio * (edge * (-3 - 2 * rootThree) / 4 - (edge * (-3 - rootThree) / 2))", "edge * (-1 - rootThree) / 2 + starDepthRatio * (edge * (-2 - rootThree) / 4 - (edge * (-1 - rootThree) / 2))"], ["edge * (-1 - rootThree) / 2", "edge * (-1 - rootThree) / 2"], ["-edge / 2", "edge * (-2 - rootThree) / 2"], ["0", "edge * (-1 - rootThree) + starDepthRatio * (edge * (-2 - rootThree) / 2 - (edge * (-1 - rootThree)))"], ["edge / 2", "edge * (-2 - rootThree) / 2"], ["edge * (1 + rootThree) / 2", "edge * (-1 - rootThree) / 2"], ["edge * (3 + rootThree) / 2 + starDepthRatio * (edge * (3 + 2 * rootThree) / 4 - (edge * (3 + rootThree) / 2))", "edge * (-1 - rootThree) / 2 + starDepthRatio * (edge * (-2 - rootThree) / 4 - (edge * (-1 - rootThree) / 2))"], ["edge * (2 + rootThree) / 2", "-edge / 2"] ] }, { "polygon": [ ["edge * (-2 - rootThree) / 2", "edge / 2"], ["edge * (-3 - rootThree) / 2 + starDepthRatio * (edge * (-3 - 2 * rootThree) / 4 - (edge * (-3 - rootThree) / 2))", "edge * (1 + rootThree) / 2 + starDepthRatio * (edge * (2 + rootThree) / 4 - (edge * (1 + rootThree) / 2))"], ["edge * (-1 - rootThree) / 2", "edge * (1 + rootThree) / 2"], ["edge * (-3 - rootThree) / 2 + starDepthRatio * (edge * (-3 - 2 * rootThree) / 4 - (edge * (-3 - rootThree) / 2))", "edge * (1 + rootThree) / 2 + starDepthRatio * (edge * (2 + 3 * rootThree) / 4 - (edge * (1 + rootThree) / 2))"], ["edge * (-2 - rootThree) / 2", "edge * (1 + 2 * rootThree) / 2"], ["edge * (-3 - rootThree) / 2 + starDepthRatio * (edge * (-3 - rootThree) / 2 - (edge * (-3 - rootThree) / 2))", "edge * (1 + rootThree) / 2 + starDepthRatio * (edge * (1 + 2 * rootThree) / 2 - (edge * (1 + rootThree) / 2))"], ["edge * (-4 - rootThree) / 2", "edge * (1 + 2 * rootThree) / 2"], ["edge * (-3 - rootThree) / 2 + starDepthRatio * (edge * (-9 - 2 * rootThree) / 4 - (edge * (-3 - rootThree) / 2))", "edge * (1 + rootThree) / 2 + starDepthRatio * (edge * (2 + 3 * rootThree) / 4 - (edge * (1 + rootThree) / 2))"], ["edge * (-5 - rootThree) / 2", "edge * (1 + rootThree) / 2"], ["edge * (-3 - rootThree) / 2 + starDepthRatio * (edge * (-9 - 2 * rootThree) / 4 - (edge * (-3 - rootThree) / 2))", "edge * (1 + rootThree) / 2 + starDepthRatio * (edge * (2 + rootThree) / 4 - (edge * (1 + rootThree) / 2))"], ["edge * (-4 - rootThree) / 2", "edge / 2"], ["edge * (-3 - rootThree) / 2 + starDepthRatio * (edge * (-3 - rootThree) / 2 - (edge * (-3 - rootThree) / 2))", "edge * (1 + rootThree) / 2 + starDepthRatio * (edge / 2 - (edge * (1 + rootThree) / 2))"] ] }, { "polygon": [ ["-edge / 2", "edge * (-2 - rootThree) / 2"], ["edge * (-1 - rootThree) / 2", "edge * (-1 - rootThree) / 2"], ["edge * (-3 - rootThree) / 2 + starDepthRatio * (edge * (-3 - 2 * rootThree) / 4 - (edge * (-3 - rootThree) / 2))", "edge * (-1 - rootThree) / 2 + starDepthRatio * (edge * (-2 - 3 * rootThree) / 4 - (edge * (-1 - rootThree) / 2))"], ["edge * (-2 - rootThree) / 2", "edge * (-1 - 2 * rootThree) / 2"], ["-edge", "edge * (-1 - rootThree)"], ["starDepthRatio * (-3 * edge / 4)", "edge * (-1 - rootThree) + starDepthRatio * (edge * (-4 - 3 * rootThree) / 4 - (edge * (-1 - rootThree)))"] ] }, { "polygon": [ ["edge * (-1 - rootThree) / 2", "edge * (-1 - rootThree) / 2"], ["edge * (-3 - rootThree) / 2 + starDepthRatio * (edge * (-3 - 2 * rootThree) / 4 - (edge * (-3 - rootThree) / 2))", "edge * (-1 - rootThree) / 2 + starDepthRatio * (edge * (-2 - rootThree) / 4 - (edge * (-1 - rootThree) / 2))"], ["edge * (-2 - rootThree) / 2", "-edge / 2"], ["edge * (-3 - rootThree) / 2 + starDepthRatio * (edge * (-3 - rootThree) / 2 - (edge * (-3 - rootThree) / 2))", "edge * (-1 - rootThree) / 2 + starDepthRatio * (-edge / 2 - (edge * (-1 - rootThree) / 2))"], ["edge * (-4 - rootThree) / 2", "-edge / 2"], ["edge * (-3 - rootThree) / 2 + starDepthRatio * (edge * (-9 - 2 * rootThree) / 4 - (edge * (-3 - rootThree) / 2))", "edge * (-1 - rootThree) / 2 + starDepthRatio * (edge * (-2 - rootThree) / 4 - (edge * (-1 - rootThree) / 2))"], ["edge * (-5 - rootThree) / 2", "edge * (-1 - rootThree) / 2"], ["edge * (-3 - rootThree) / 2 + starDepthRatio * (edge * (-9 - 2 * rootThree) / 4 - (edge * (-3 - rootThree) / 2))", "edge * (-1 - rootThree) / 2 + starDepthRatio * (edge * (-2 - 3 * rootThree) / 4 - (edge * (-1 - rootThree) / 2))"], ["edge * (-4 - rootThree) / 2", "edge * (-1 - 2 * rootThree) / 2"], ["edge * (-3 - rootThree) / 2 + starDepthRatio * (edge * (-3 - rootThree) / 2 - (edge * (-3 - rootThree) / 2))", "edge * (-1 - rootThree) / 2 + starDepthRatio * (edge * (-1 - 2 * rootThree) / 2 - (edge * (-1 - rootThree) / 2))"], ["edge * (-2 - rootThree) / 2", "edge * (-1 - 2 * rootThree) / 2"], ["edge * (-3 - rootThree) / 2 + starDepthRatio * (edge * (-3 - 2 * rootThree) / 4 - (edge * (-3 - rootThree) / 2))", "edge * (-1 - rootThree) / 2 + starDepthRatio * (edge * (-2 - 3 * rootThree) / 4 - (edge * (-1 - rootThree) / 2))"] ] }, { "polygon": [ ["-edge", "edge * (1 + rootThree)"], ["edge * (-2 - rootThree) / 2", "edge * (1 + 2 * rootThree) / 2"], ["edge * (-3 - rootThree) / 2 + starDepthRatio * (edge * (-3 - 2 * rootThree) / 4 - (edge * (-3 - rootThree) / 2))", "edge * (1 + rootThree) / 2 + starDepthRatio * (edge * (2 + 3 * rootThree) / 4 - (edge * (1 + rootThree) / 2))"], ["edge * (-1 - rootThree) / 2", "edge * (1 + rootThree) / 2"], ["-edge / 2", "edge * (2 + rootThree) / 2"], ["starDepthRatio * (-3 * edge / 4)", "edge * (1 + rootThree) + starDepthRatio * (edge * (4 + 3 * rootThree) / 4 - (edge * (1 + rootThree)))"] ] }, { "polygon": [ ["edge * (-4 - rootThree) / 2", "edge / 2"], ["edge * (-4 - rootThree) / 2", "-edge / 2"], ["edge * (-3 - rootThree) / 2 + starDepthRatio * (edge * (-3 - rootThree) / 2 - (edge * (-3 - rootThree) / 2))", "edge * (-1 - rootThree) / 2 + starDepthRatio * (-edge / 2 - (edge * (-1 - rootThree) / 2))"], ["edge * (-2 - rootThree) / 2", "-edge / 2"], ["edge * (-2 - rootThree) / 2", "edge / 2"], ["edge * (-3 - rootThree) / 2 + starDepthRatio * (edge * (-3 - rootThree) / 2 - (edge * (-3 - rootThree) / 2))", "edge * (1 + rootThree) / 2 + starDepthRatio * (edge / 2 - (edge * (1 + rootThree) / 2))"] ] } ], "lattice": { "a": ["edge * (3 + rootThree)", "0"], "b": ["edge * (3 + rootThree) / 2", "edge * (3 + 3 * rootThree) / 2"] } } ,"hexagram-rhombus":{ "schema": 1, "id": "hexagram-rhombus", "name": "Hexagram and rhombus", "category": "ceramic", "parameters": { "edge": {"value": 100, "min": 10, "max": 500, "label": "Edge"}, "starDepthRatio": { "expr": "0.666667" }, "rootThree": {"expr": "sqrt(3)"} }, "tiles": [ { "polygon": [ ["edge", "0"], ["starDepthRatio * (3 * edge / 4)", "starDepthRatio * (rootThree * edge / 4)"], ["edge / 2", "rootThree * edge / 2"], ["0", "starDepthRatio * (rootThree * edge / 2)"], ["-edge / 2", "rootThree * edge / 2"], ["starDepthRatio * (-3 * edge / 4)", "starDepthRatio * (rootThree * edge / 4)"], ["-edge", "0"], ["starDepthRatio * (-3 * edge / 4)", "starDepthRatio * (-rootThree * edge / 4)"], ["-edge / 2", "-rootThree * edge / 2"], ["0", "starDepthRatio * (-rootThree * edge / 2)"], ["edge / 2", "-rootThree * edge / 2"], ["starDepthRatio * (3 * edge / 4)", "starDepthRatio * (-rootThree * edge / 4)"] ] }, { "polygon": [ ["-edge", "0"], ["starDepthRatio * (-3 * edge / 4)", "starDepthRatio * (-rootThree * edge / 4)"], ["-edge / 2", "-rootThree * edge / 2"], ["-3 * edge / 2 + starDepthRatio * (-3 * edge / 4 - (-3 * edge / 2))", "-rootThree * edge / 2 + starDepthRatio * (-rootThree * edge / 4 - (-rootThree * edge / 2))"] ] }, { "polygon": [ ["-edge / 2", "-rootThree * edge / 2"], ["0", "starDepthRatio * (-rootThree * edge / 2)"], ["edge / 2", "-rootThree * edge / 2"], ["0", "-rootThree * edge + starDepthRatio * (-rootThree * edge / 2 - (-rootThree * edge))"] ] }, { "polygon": [ ["-edge / 2", "rootThree * edge / 2"], ["starDepthRatio * (-3 * edge / 4)", "starDepthRatio * (rootThree * edge / 4)"], ["-edge", "0"], ["-3 * edge / 2 + starDepthRatio * (-3 * edge / 4 - (-3 * edge / 2))", "rootThree * edge / 2 + starDepthRatio * (rootThree * edge / 4 - (rootThree * edge / 2))"] ] } ], "lattice": { "a": ["3 * edge / 2", "rootThree * edge / 2"], "b": ["0", "rootThree * edge"] } } ,"hexagram-snub":{ "schema": 1, "id": "hexagram-snub", "name": "Hexagram and snub triangles", "category": "ceramic", "parameters": { "edge": {"value": 100, "min": 10, "max": 500, "label": "Edge"}, "starDepthRatio": { "expr": "0.666667" }, "rootThree": {"expr": "sqrt(3)"} }, "tiles": [ { "polygon": [ ["edge", "0"], ["starDepthRatio * (3 * edge / 4)", "starDepthRatio * (rootThree * edge / 4)"], ["edge / 2", "rootThree * edge / 2"], ["0", "starDepthRatio * (rootThree * edge / 2)"], ["-edge / 2", "rootThree * edge / 2"], ["starDepthRatio * (-3 * edge / 4)", "starDepthRatio * (rootThree * edge / 4)"], ["-edge", "0"], ["starDepthRatio * (-3 * edge / 4)", "starDepthRatio * (-rootThree * edge / 4)"], ["-edge / 2", "-rootThree * edge / 2"], ["0", "starDepthRatio * (-rootThree * edge / 2)"], ["edge / 2", "-rootThree * edge / 2"], ["starDepthRatio * (3 * edge / 4)", "starDepthRatio * (-rootThree * edge / 4)"] ] }, { "polygon": [ ["3 * edge / 2", "rootThree * edge / 2"], ["edge / 2", "rootThree * edge / 2"], ["starDepthRatio * (3 * edge / 4)", "starDepthRatio * (rootThree * edge / 4)"], ["edge", "0"] ] }, { "polygon": [ ["-edge / 2", "-rootThree * edge / 2"], ["starDepthRatio * (-3 * edge / 4)", "starDepthRatio * (-rootThree * edge / 4)"], ["-edge", "0"], ["-3 * edge / 2", "-rootThree * edge / 2"] ] }, { "polygon": [ ["0", "rootThree * edge"], ["-edge / 2", "rootThree * edge / 2"], ["0", "starDepthRatio * (rootThree * edge / 2)"], ["edge / 2", "rootThree * edge / 2"] ] }, { "polygon": [ ["edge / 2", "-rootThree * edge / 2"], ["0", "starDepthRatio * (-rootThree * edge / 2)"], ["-edge / 2", "-rootThree * edge / 2"], ["0", "-rootThree * edge"] ] }, { "polygon": [ ["-edge", "0"], ["-3 * edge / 2", "rootThree * edge / 2"], ["-2 * edge", "0"] ] }, { "polygon": [ ["edge", "0"], ["starDepthRatio * (3 * edge / 4)", "starDepthRatio * (-rootThree * edge / 4)"], ["edge / 2", "-rootThree * edge / 2"], ["3 * edge / 2", "-rootThree * edge / 2"] ] }, { "polygon": [ ["-3 * edge / 2", "-rootThree * edge / 2"], ["-edge", "-rootThree * edge"], ["-edge / 2", "-rootThree * edge / 2"] ] }, { "polygon": [ ["-edge", "0"], ["starDepthRatio * (-3 * edge / 4)", "starDepthRatio * (rootThree * edge / 4)"], ["-edge / 2", "rootThree * edge / 2"], ["-3 * edge / 2", "rootThree * edge / 2"] ] } ], "lattice": { "a": ["5 * edge / 2", "rootThree * edge / 2"], "b": ["edge / 2", "3 * rootThree * edge / 2"] } } ,"hexagram-square-triangle":{ "schema": 1, "id": "hexagram-square-triangle", "name": "Hexagram, square and triangle", "category": "ceramic", "parameters": { "edge": {"value": 60, "min": 10, "max": 500, "label": "Edge"}, "starDepthRatio": { "expr": "0.666667" }, "rootThree": {"expr": "sqrt(3)"} }, "tiles": [ { "polygon": [ ["edge", "0"], ["starDepthRatio * (3 * edge / 4)", "starDepthRatio * (rootThree * edge / 4)"], ["edge / 2", "rootThree * edge / 2"], ["0", "starDepthRatio * (rootThree * edge / 2)"], ["-edge / 2", "rootThree * edge / 2"], ["starDepthRatio * (-3 * edge / 4)", "starDepthRatio * (rootThree * edge / 4)"], ["-edge", "0"], ["starDepthRatio * (-3 * edge / 4)", "starDepthRatio * (-rootThree * edge / 4)"], ["-edge / 2", "-rootThree * edge / 2"], ["0", "starDepthRatio * (-rootThree * edge / 2)"], ["edge / 2", "-rootThree * edge / 2"], ["starDepthRatio * (3 * edge / 4)", "starDepthRatio * (-rootThree * edge / 4)"] ] }, { "polygon": [ ["-edge / 2", "-rootThree * 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"cellSize * (6 - sqrt(2)) / 8"] ] }, { "polygon": [ ["cellSize * (5 + sqrt(2)) / 8", "cellSize * 5 / 8"], ["cellSize * 3 / 4", "cellSize * (6 - sqrt(2)) / 8"], ["cellSize * (8 - sqrt(2)) / 8", "cellSize / 2"], ["cellSize * 7 / 8", "cellSize * (3 + sqrt(2)) / 8"], ["cellSize * 7 / 8", "cellSize * 5 / 8"] ] }, { "polygon": [ ["cellSize / 8", "cellSize * 5 / 8"], ["cellSize / 8", "cellSize * (3 + sqrt(2)) / 8"], ["cellSize * sqrt(2) / 8", "cellSize / 2"], ["cellSize / 4", "cellSize * (6 - sqrt(2)) / 8"], ["cellSize * (3 - sqrt(2)) / 8", "cellSize * 5 / 8"] ] }, { "polygon": [ ["cellSize / 4", "0"], ["cellSize * (1 + sqrt(2)) / 8", "-cellSize / 8"], ["cellSize * 3 / 8", "-cellSize / 8"], ["cellSize * 3 / 8", "cellSize * (1 - sqrt(2)) / 8"], ["cellSize * (4 - sqrt(2)) / 8", "0"], ["cellSize * 3 / 8", "cellSize * (-1 + sqrt(2)) / 8"], ["cellSize * 3 / 8", "cellSize / 8"], ["cellSize * (1 + sqrt(2)) / 8", "cellSize / 8"] ] }, { "polygon": [ ["cellSize * (4 + sqrt(2)) / 8", "0"], ["cellSize * 5 / 8", "cellSize * (-1 + sqrt(2)) / 8"], ["cellSize * 5 / 8", "cellSize / 8"], ["cellSize * (3 + sqrt(2)) / 8", "cellSize / 8"], ["cellSize / 2", "cellSize * sqrt(2) / 8"], ["cellSize * (5 - sqrt(2)) / 8", "cellSize / 8"], ["cellSize * 3 / 8", "cellSize / 8"], ["cellSize * 3 / 8", "cellSize * (-1 + sqrt(2)) / 8"], ["cellSize * (4 - sqrt(2)) / 8", "0"], ["cellSize * 3 / 8", "cellSize * (1 - sqrt(2)) / 8"], ["cellSize * 3 / 8", "-cellSize / 8"], ["cellSize * (5 - sqrt(2)) / 8", "-cellSize / 8"], ["cellSize / 2", "cellSize * -sqrt(2) / 8"], ["cellSize * (3 + sqrt(2)) / 8", "-cellSize / 8"], ["cellSize * 5 / 8", "-cellSize / 8"], ["cellSize * 5 / 8", "cellSize * (1 - sqrt(2)) / 8"] ] }, { "polygon": [ ["cellSize * 3 / 4", "cellSize * (6 - sqrt(2)) / 8"], ["cellSize * (4 + sqrt(2)) / 8", "cellSize / 2"], ["cellSize * 3 / 4", "cellSize * (2 + sqrt(2)) / 8"], ["cellSize * (8 - sqrt(2)) / 8", "cellSize / 2"] ] }, { "polygon": [ ["cellSize / 4", "cellSize * (6 - sqrt(2)) / 8"], ["cellSize * (4 - sqrt(2)) / 8", "cellSize / 2"], ["cellSize * 3 / 8", "cellSize * (3 + sqrt(2)) / 8"], ["cellSize * 3 / 8", "cellSize * 5 / 8"], ["cellSize * (1 + sqrt(2)) / 8", "cellSize * 5 / 8"] ] }, { "polygon": [ ["cellSize / 4", "cellSize * (6 - sqrt(2)) / 8"], ["cellSize * sqrt(2) / 8", "cellSize / 2"], ["cellSize / 4", "cellSize * (2 + sqrt(2)) / 8"], ["cellSize * (4 - sqrt(2)) / 8", "cellSize / 2"] ] }, { "polygon": [ ["cellSize / 4", "cellSize * (2 + sqrt(2)) / 8"], ["cellSize * (1 + sqrt(2)) / 8", "cellSize * 3 / 8"], ["cellSize * 3 / 8", "cellSize * 3 / 8"], ["cellSize * 3 / 8", "cellSize * (5 - sqrt(2)) / 8"], ["cellSize * (4 - sqrt(2)) / 8", "cellSize / 2"] ] }, { "polygon": [ ["cellSize * 5 / 8", "cellSize * (5 - sqrt(2)) / 8"], ["cellSize * (4 + sqrt(2)) / 8", "cellSize / 2"], ["cellSize * 5 / 8", "cellSize * (3 + sqrt(2)) / 8"], ["cellSize * 5 / 8", "cellSize * 5 / 8"], ["cellSize * (3 + sqrt(2)) / 8", "cellSize * 5 / 8"], ["cellSize / 2", "cellSize * (4 + sqrt(2)) / 8"], ["cellSize * (5 - sqrt(2)) / 8", "cellSize * 5 / 8"], ["cellSize * 3 / 8", "cellSize * 5 / 8"], ["cellSize * 3 / 8", "cellSize * (3 + sqrt(2)) / 8"], ["cellSize * (4 - sqrt(2)) / 8", "cellSize / 2"], ["cellSize * 3 / 8", "cellSize * (5 - sqrt(2)) / 8"], ["cellSize * 3 / 8", "cellSize * 3 / 8"], ["cellSize * (5 - sqrt(2)) / 8", "cellSize * 3 / 8"], ["cellSize / 2", "cellSize * (4 - sqrt(2)) / 8"], ["cellSize * (3 + sqrt(2)) / 8", "cellSize * 3 / 8"], ["cellSize * 5 / 8", "cellSize * 3 / 8"] ] }, { "polygon": [ ["cellSize * 5 / 8", "cellSize * 3 / 8"], ["cellSize * (3 + sqrt(2)) / 8", "cellSize * 3 / 8"], ["cellSize / 2", "cellSize * (4 - sqrt(2)) / 8"], ["cellSize * (6 - sqrt(2)) / 8", "cellSize / 4"], ["cellSize * 5 / 8", "cellSize * (1 + sqrt(2)) / 8"] ] }, { "polygon": [ ["cellSize * 5 / 8", "cellSize * (3 - sqrt(2)) / 8"], ["cellSize * (6 - sqrt(2)) / 8", "cellSize / 4"], ["cellSize / 2", "cellSize * sqrt(2) / 8"], ["cellSize * (3 + sqrt(2)) / 8", "cellSize / 8"], ["cellSize * 5 / 8", "cellSize / 8"] ] }, { "polygon": [ ["cellSize * 5 / 8", "cellSize * 7 / 8"], ["cellSize * (3 + sqrt(2)) / 8", "cellSize * 7 / 8"], ["cellSize / 2", "cellSize * (8 - sqrt(2)) / 8"], ["cellSize * (6 - sqrt(2)) / 8", "cellSize * 3 / 4"], ["cellSize * 5 / 8", "cellSize * (5 + sqrt(2)) / 8"] ] }, { "polygon": [ ["cellSize * 5 / 8", "cellSize * (7 - sqrt(2)) / 8"], ["cellSize * (6 - sqrt(2)) / 8", "cellSize * 3 / 4"], ["cellSize / 2", "cellSize * (4 + sqrt(2)) / 8"], ["cellSize * (3 + sqrt(2)) / 8", "cellSize * 5 / 8"], ["cellSize * 5 / 8", "cellSize * 5 / 8"] ] }, { "polygon": [ ["cellSize * (6 - sqrt(2)) / 8", "cellSize / 4"], ["cellSize / 2", "cellSize * (4 - sqrt(2)) / 8"], ["cellSize * (2 + sqrt(2)) / 8", "cellSize / 4"], ["cellSize / 2", "cellSize * sqrt(2) / 8"] ] }, { "polygon": [ ["cellSize * (6 - sqrt(2)) / 8", "cellSize * 3 / 4"], ["cellSize / 2", "cellSize * (8 - sqrt(2)) / 8"], ["cellSize * (2 + sqrt(2)) / 8", "cellSize * 3 / 4"], ["cellSize / 2", "cellSize * (4 + sqrt(2)) / 8"] ] }, { "polygon": [ ["cellSize * 3 / 8", "cellSize * 5 / 8"], ["cellSize * (5 - sqrt(2)) / 8", "cellSize * 5 / 8"], ["cellSize / 2", "cellSize * (4 + sqrt(2)) / 8"], ["cellSize * (2 + sqrt(2)) / 8", "cellSize * 3 / 4"], ["cellSize * 3 / 8", "cellSize * (7 - sqrt(2)) / 8"] ] }, { "polygon": [ ["cellSize * 3 / 8", "cellSize * (5 + sqrt(2)) / 8"], ["cellSize * (2 + sqrt(2)) / 8", "cellSize * 3 / 4"], ["cellSize / 2", "cellSize * (8 - sqrt(2)) / 8"], ["cellSize * (5 - sqrt(2)) / 8", "cellSize * 7 / 8"], ["cellSize * 3 / 8", "cellSize * 7 / 8"] ] }, { "polygon": [ ["cellSize * 3 / 8", "cellSize / 8"], ["cellSize * (5 - sqrt(2)) / 8", "cellSize / 8"], ["cellSize / 2", "cellSize * sqrt(2) / 8"], ["cellSize * (2 + sqrt(2)) / 8", "cellSize / 4"], ["cellSize * 3 / 8", "cellSize * (3 - sqrt(2)) / 8"] ] }, { "polygon": [ ["cellSize * 3 / 8", "cellSize * (1 + sqrt(2)) / 8"], ["cellSize * (2 + sqrt(2)) / 8", "cellSize / 4"], ["cellSize / 2", "cellSize * (4 - sqrt(2)) / 8"], ["cellSize * (5 - sqrt(2)) / 8", "cellSize * 3 / 8"], ["cellSize * 3 / 8", "cellSize * 3 / 8"] ] } ], "lattice": { "a": ["cellSize", "0"], "b": ["0", "cellSize"] } } ,"octagon-eight-star-pmm":{ "schema": 1, "id": "octagon-eight-star-pmm", "name": "Eight-point star rosettes with octagons", "category": "ceramic", "parameters": { "cellSize": {"value": 160, "min": 60, "max": 600, "label": "Cell width"}, "halfBandWidth": {"expr": "cellSize / (2 / cos(22.5) + 4 * sqrt(2))"}, "starOuterRadius": {"expr": "halfBandWidth * sqrt(2)"}, "starInnerRadius": {"expr": "starOuterRadius * cos(45) / cos(22.5)"}, "smallOctagonRadius": {"expr": "cellSize * (sqrt(2) - 1) / 2"} }, "tiles": [ { "polygon": [ ["starOuterRadius * cos(0)", "starOuterRadius * sin(0)"], ["starInnerRadius * cos(22.5)", "starInnerRadius * sin(22.5)"], ["starOuterRadius * cos(45)", "starOuterRadius * sin(45)"], ["starInnerRadius * cos(67.5)", "starInnerRadius * sin(67.5)"], ["starOuterRadius * cos(90)", "starOuterRadius * sin(90)"], ["starInnerRadius * cos(112.5)", "starInnerRadius * sin(112.5)"], ["starOuterRadius * cos(135)", "starOuterRadius * sin(135)"], ["starInnerRadius * cos(157.5)", "starInnerRadius * sin(157.5)"], ["starOuterRadius * cos(180)", "starOuterRadius * sin(180)"], ["starInnerRadius * cos(202.5)", "starInnerRadius * sin(202.5)"], ["starOuterRadius * cos(225)", "starOuterRadius * sin(225)"], ["starInnerRadius * cos(247.5)", "starInnerRadius * sin(247.5)"], ["starOuterRadius * cos(270)", "starOuterRadius * sin(270)"], ["starInnerRadius * cos(292.5)", "starInnerRadius * sin(292.5)"], ["starOuterRadius * cos(315)", "starOuterRadius * sin(315)"], ["starInnerRadius * cos(337.5)", "starInnerRadius * sin(337.5)"] ] }, { "repeat": {"index": "k", "count": "8"}, "transform": [{"rotate": {"angle": "45 * k", "center": ["0", "0"]}}], "polygon": [ ["starOuterRadius", "0"], ["halfBandWidth * (1 + sqrt(2))", "-halfBandWidth"], ["cellSize / 2 - halfBandWidth * (sqrt(2) - 1)", "-halfBandWidth"], ["cellSize / 2", "0"], ["cellSize / 2 - halfBandWidth * (sqrt(2) - 1)", "halfBandWidth"], ["halfBandWidth * (1 + sqrt(2))", "halfBandWidth"] ] }, { "repeat": {"index": "k", "count": "8"}, "transform": [{"rotate": {"angle": "45 * k", "center": ["0", "0"]}}], "polygon": [ ["halfBandWidth", "halfBandWidth * (sqrt(2) - 1)"], ["starOuterRadius", "0"], ["halfBandWidth * (1 + sqrt(2))", "halfBandWidth"], ["halfBandWidth", "halfBandWidth"] ] }, { "polygon": [ ["smallOctagonRadius * cos(0)", "cellSize * sqrt(2) / 2 + smallOctagonRadius * sin(0)"], ["smallOctagonRadius * cos(45)", "cellSize * sqrt(2) / 2 + smallOctagonRadius * sin(45)"], ["smallOctagonRadius * cos(90)", "cellSize * sqrt(2) / 2 + smallOctagonRadius * sin(90)"], ["smallOctagonRadius * cos(135)", "cellSize * sqrt(2) / 2 + smallOctagonRadius * sin(135)"], ["smallOctagonRadius * cos(180)", "cellSize * sqrt(2) / 2 + smallOctagonRadius * sin(180)"], ["smallOctagonRadius * cos(225)", "cellSize * sqrt(2) / 2 + smallOctagonRadius * sin(225)"], ["smallOctagonRadius * cos(270)", "cellSize * sqrt(2) / 2 + smallOctagonRadius * sin(270)"], ["smallOctagonRadius * cos(315)", "cellSize * sqrt(2) / 2 + smallOctagonRadius * sin(315)"] ] }, { "polygon": [ ["cellSize / 2 + smallOctagonRadius * cos(0)", "cellSize / 2 + smallOctagonRadius * sin(0)"], ["cellSize / 2 + smallOctagonRadius * cos(45)", "cellSize / 2 + smallOctagonRadius * sin(45)"], ["cellSize / 2 + smallOctagonRadius * cos(90)", "cellSize / 2 + smallOctagonRadius * sin(90)"], ["cellSize / 2 + smallOctagonRadius * cos(135)", "cellSize / 2 + smallOctagonRadius * sin(135)"], ["cellSize / 2 + smallOctagonRadius * cos(180)", "cellSize / 2 + smallOctagonRadius * sin(180)"], ["cellSize / 2 + smallOctagonRadius * cos(225)", "cellSize / 2 + smallOctagonRadius * sin(225)"], ["cellSize / 2 + smallOctagonRadius * cos(270)", "cellSize / 2 + smallOctagonRadius * sin(270)"], ["cellSize / 2 + smallOctagonRadius * cos(315)", "cellSize / 2 + smallOctagonRadius * sin(315)"] ] }, { "polygon": [ ["cellSize / 2 + smallOctagonRadius * cos(0)", "-cellSize / 2 + smallOctagonRadius * sin(0)"], ["cellSize / 2 + smallOctagonRadius * cos(45)", "-cellSize / 2 + smallOctagonRadius * sin(45)"], ["cellSize / 2 + smallOctagonRadius * cos(90)", "-cellSize / 2 + smallOctagonRadius * sin(90)"], ["cellSize / 2 + smallOctagonRadius * cos(135)", "-cellSize / 2 + smallOctagonRadius * sin(135)"], ["cellSize / 2 + smallOctagonRadius * cos(180)", "-cellSize / 2 + smallOctagonRadius * sin(180)"], ["cellSize / 2 + smallOctagonRadius * cos(225)", "-cellSize / 2 + smallOctagonRadius * sin(225)"], ["cellSize / 2 + smallOctagonRadius * cos(270)", "-cellSize / 2 + smallOctagonRadius * sin(270)"], ["cellSize / 2 + smallOctagonRadius * cos(315)", "-cellSize / 2 + smallOctagonRadius * sin(315)"] ] }, { "polygon": [ ["-halfBandWidth", "cellSize * sqrt(2) + halfBandWidth * (-1 - sqrt(2))"], ["-halfBandWidth", "cellSize * (-1 + 2 * sqrt(2)) / 2 + halfBandWidth * (-2 + 2 * sqrt(2)) / 2"], ["0", "cellSize * (-1 + 2 * sqrt(2)) / 2"], ["cellSize * (-2 + sqrt(2)) / 4", "cellSize * (2 + sqrt(2)) / 4"], ["cellSize * (1 - sqrt(2)) / 2", "cellSize * sqrt(2) / 2"], ["cellSize * (-2 + sqrt(2)) / 4", "cellSize * (-2 + 3 * sqrt(2)) / 4"], ["0", "cellSize / 2"], ["-halfBandWidth", "cellSize / 2 + halfBandWidth * (2 - 2 * sqrt(2)) / 2"], ["-halfBandWidth", "halfBandWidth * (1 + sqrt(2))"], ["cellSize * -sqrt(2) / 4 + halfBandWidth * 4 / 4", "cellSize * sqrt(2) / 4 + halfBandWidth * (-4 + 4 * sqrt(2)) / 4"], ["cellSize * -sqrt(2) / 4", "cellSize * sqrt(2) / 4"], ["cellSize * (-2 + sqrt(2)) / 2", "cellSize / 2"], ["cellSize * -sqrt(2) / 4", "cellSize * (4 - sqrt(2)) / 4"], ["-cellSize / 2", "cellSize * sqrt(2) / 2"], ["cellSize * -sqrt(2) / 4", "cellSize * (-4 + 5 * sqrt(2)) / 4"], ["cellSize * (-2 + sqrt(2)) / 2", "cellSize * (-1 + 2 * sqrt(2)) / 2"], ["cellSize * -sqrt(2) / 4", "cellSize * 3 * sqrt(2) / 4"], ["cellSize * -sqrt(2) / 4 + halfBandWidth * 4 / 4", "cellSize * 3 * sqrt(2) / 4 + halfBandWidth * (4 - 4 * sqrt(2)) / 4"] ] }, { "polygon": [ ["0", "cellSize * (-1 + 2 * sqrt(2)) / 2"], ["halfBandWidth", "cellSize * (-1 + 2 * sqrt(2)) / 2 + halfBandWidth * (-2 + 2 * sqrt(2)) / 2"], ["halfBandWidth", "cellSize * sqrt(2) + halfBandWidth * (-1 - sqrt(2))"], ["cellSize * sqrt(2) / 4 + halfBandWidth * -4 / 4", "cellSize * 3 * sqrt(2) / 4 + halfBandWidth * (4 - 4 * sqrt(2)) / 4"], ["cellSize * sqrt(2) / 4", "cellSize * 3 * sqrt(2) / 4"], ["cellSize * (2 - sqrt(2)) / 2", "cellSize * (-1 + 2 * sqrt(2)) / 2"], ["cellSize * sqrt(2) / 4", "cellSize * (-4 + 5 * sqrt(2)) / 4"], ["cellSize / 2", "cellSize * sqrt(2) / 2"], ["cellSize * sqrt(2) / 4", "cellSize * (4 - sqrt(2)) / 4"], ["cellSize * (2 - sqrt(2)) / 2", "cellSize / 2"], ["cellSize * sqrt(2) / 4", "cellSize * sqrt(2) / 4"], ["cellSize * sqrt(2) / 4 + halfBandWidth * -4 / 4", "cellSize * sqrt(2) / 4 + halfBandWidth * (-4 + 4 * sqrt(2)) / 4"], ["halfBandWidth", "halfBandWidth * (1 + sqrt(2))"], ["halfBandWidth", "cellSize / 2 + halfBandWidth * (2 - 2 * sqrt(2)) / 2"], ["0", "cellSize / 2"], ["cellSize * (2 - sqrt(2)) / 4", "cellSize * (-2 + 3 * sqrt(2)) / 4"], ["cellSize * (-1 + sqrt(2)) / 2", "cellSize * sqrt(2) / 2"], ["cellSize * (2 - sqrt(2)) / 4", "cellSize * (2 + sqrt(2)) / 4"] ] }, { "polygon": [ ["halfBandWidth * (1 + sqrt(2))", "halfBandWidth"], ["cellSize * sqrt(2) / 4 + halfBandWidth * (-4 + 4 * sqrt(2)) / 4", "cellSize * sqrt(2) / 4 + halfBandWidth * -4 / 4"], ["cellSize * sqrt(2) / 4", "cellSize * sqrt(2) / 4"], ["cellSize / 2", "cellSize * (2 - sqrt(2)) / 2"], ["cellSize * (4 - sqrt(2)) / 4", "cellSize * sqrt(2) / 4"], ["cellSize * (4 - sqrt(2)) / 4 + halfBandWidth * (4 - 4 * sqrt(2)) / 4", "cellSize * sqrt(2) / 4 + halfBandWidth * -4 / 4"], ["cellSize + halfBandWidth * (-1 - sqrt(2))", "halfBandWidth"], ["cellSize / 2 + halfBandWidth * (-2 + 2 * sqrt(2)) / 2", "halfBandWidth"], ["cellSize / 2", "0"], ["cellSize / 2 + halfBandWidth * (2 - 2 * sqrt(2)) / 2", "halfBandWidth"] ] }, { "polygon": [ ["cellSize * (4 - sqrt(2)) / 4", "cellSize * -sqrt(2) / 4"], ["cellSize / 2", "cellSize * (-2 + sqrt(2)) / 2"], ["cellSize * sqrt(2) / 4", "cellSize * -sqrt(2) / 4"], ["cellSize * sqrt(2) / 4 + halfBandWidth * (-4 + 4 * sqrt(2)) / 4", "cellSize * -sqrt(2) / 4 + halfBandWidth * 4 / 4"], ["halfBandWidth * (1 + sqrt(2))", "-halfBandWidth"], ["cellSize / 2 + halfBandWidth * (2 - 2 * sqrt(2)) / 2", "-halfBandWidth"], ["cellSize / 2", "0"], ["cellSize / 2 + halfBandWidth * (-2 + 2 * sqrt(2)) / 2", "-halfBandWidth"], ["cellSize + halfBandWidth * (-1 - sqrt(2))", "-halfBandWidth"], ["cellSize * (4 - sqrt(2)) / 4 + halfBandWidth * (4 - 4 * sqrt(2)) / 4", "cellSize * -sqrt(2) / 4 + halfBandWidth * 4 / 4"] ] } ], "lattice": { "a": ["cellSize", "0"], "b": ["0", "cellSize * sqrt(2)"] } } ,"octagon-picket":{ "schema": 1, "id": "octagon-picket", "name": "Octagon picket", "category": "ceramic", "parameters": { "edge": { "value": 200, "min": 20, "max": 1200, "label": "Octagon side" }, "diagonal": { "expr": "edge * sqrt(2)" } }, "tiles": [ { "polygon": [ [ "1.5 * diagonal", "0.5 * diagonal" ], [ "1.5 * diagonal + 0.5 * diagonal", "0" ], [ "1.5 * diagonal + edge + 0.5 * diagonal", "0" ], [ "1.5 * diagonal + edge + diagonal", "0.5 * diagonal" ], [ "1.5 * diagonal + edge + diagonal", "edge + 0.5 * diagonal" ], [ "1.5 * diagonal + edge + 0.5 * diagonal", "edge + diagonal" ], [ "1.5 * diagonal + 0.5 * diagonal", "edge + diagonal" ], [ "1.5 * diagonal", "edge + 0.5 * diagonal" ] ] }, { "polygon": [ [ "0.5 * diagonal", "0.5 * diagonal" ], [ "diagonal", "0" ], [ "1.5 * diagonal", "0.5 * diagonal" ], [ "1.5 * diagonal", "edge + 0.5 * diagonal" ], [ "diagonal", "edge + diagonal" ], [ "0.5 * diagonal", "edge + 0.5 * diagonal" ] ], "grain": [ "0", "1" ] }, { "polygon": [ [ "1.5 * diagonal", "edge + 1.5 * diagonal" ], [ "2 * diagonal", "edge + diagonal" ], [ "edge + 2 * diagonal", "edge + diagonal" ], [ "edge + 2.5 * diagonal", "edge + 1.5 * diagonal" ], [ "edge + 2 * diagonal", "edge + 2 * diagonal" ], [ "2 * diagonal", "edge + 2 * diagonal" ] ], "grain": [ "1", "0" ] }, { "polygon": [ [ "1.5 * diagonal + 0.5 * diagonal", "edge + diagonal" ], [ "1.5 * diagonal", "edge + diagonal + 0.5 * diagonal" ], [ "1.5 * diagonal - 0.5 * diagonal", "edge + diagonal" ], [ "1.5 * diagonal", "edge + diagonal - 0.5 * diagonal" ] ] }, { "polygon": [ [ "1.5 * diagonal + 0.5 * diagonal", "0" ], [ "1.5 * diagonal", "0.5 * diagonal" ], [ "1.5 * diagonal - 0.5 * diagonal", "0" ], [ "1.5 * diagonal", "-0.5 * diagonal" ] ] }, { "polygon": [ [ "0.5 * diagonal + 0.5 * diagonal", "edge + diagonal" ], [ "0.5 * diagonal", "edge + diagonal + 0.5 * diagonal" ], [ "0.5 * diagonal - 0.5 * diagonal", "edge + diagonal" ], [ "0.5 * diagonal", "edge + diagonal - 0.5 * diagonal" ] ] }, { "polygon": [ [ "0.5 * diagonal + 0.5 * diagonal", "0" ], [ "0.5 * diagonal", "0.5 * diagonal" ], [ "0.5 * diagonal - 0.5 * diagonal", "0" ], [ "0.5 * diagonal", "-0.5 * diagonal" ] ] }, { "polygon": [ [ "diagonal + 0.5 * diagonal", "edge + 1.5 * diagonal" ], [ "diagonal", "edge + 1.5 * diagonal + 0.5 * diagonal" ], [ "diagonal - 0.5 * diagonal", "edge + 1.5 * diagonal" ], [ "diagonal", "edge + 1.5 * diagonal - 0.5 * diagonal" ] ] } ], "lattice": { "a": [ "edge + 2 * diagonal", "0" ], "b": [ "0", "edge + 2 * diagonal" ] } } ,"octagon-with-stem":{ "schema": 1, "id": "octagon-with-stem", "name": "Octagon with stem", "category": "stone", "parameters": { "edge": { "value": 75, "min": 20, "max": 200, "label": "Stem side (= flat sides)" }, "diagonalEdge": { "value": 45, "min": 10, "max": 150, "label": "Diagonal side" }, "halfEdge": { "expr": "edge / 2" }, "halfOctagonWidth": { "expr": "edge / 2 + diagonalEdge / sqrt(2)" }, "columnStep": { "expr": "2 * halfOctagonWidth + edge" } }, "tiles": [ { "polygon": [ ["halfEdge", "-halfOctagonWidth"], ["halfOctagonWidth", "-halfEdge"], ["halfOctagonWidth + edge", "-halfEdge"], ["halfOctagonWidth + edge", "halfEdge"], ["halfOctagonWidth", "halfEdge"], ["halfEdge", "halfOctagonWidth"], ["-halfEdge", "halfOctagonWidth"], ["-halfOctagonWidth", "halfEdge"], ["-halfOctagonWidth", "-halfEdge"], ["-halfEdge", "-halfOctagonWidth"] ] } ], "lattice": { "a": ["columnStep", "0"], "b": ["columnStep / 2", "columnStep / 2"] } } ,"octagram-mosaic":{ "schema": 1, "id": "octagram-mosaic", "name": "Octagram mosaic", "category": "ceramic", "parameters": { "edge": { "value": 100, "min": 20, "max": 400, "label": "Square tile side" }, "cellSize": { "expr": "edge * (2 + sqrt(2))" }, "innerRadius": { "expr": "edge * cos(45) / cos(22.5)" } }, "tiles": [ { "polygon": [ [ "edge * cos(22.5)", "cellSize / 2 + edge * sin(22.5)" ], [ "cellSize / 2", "cellSize / 2" ], [ "1 * cellSize + edge * cos(157.5)", "cellSize / 2 + edge * sin(157.5)" ], [ "cellSize / 2 + edge / 2", "1 * cellSize - edge / 2" ], [ "cellSize / 2 - edge / 2", "1 * cellSize - edge / 2" ] ] }, { "polygon": [ [ "edge * cos(292.5)", "cellSize / 2 + edge * sin(292.5)" ], [ "cellSize / 2 - edge / 2", "edge / 2" ], [ "edge * cos(337.5)", "cellSize / 2 + edge * sin(337.5)" ], [ "innerRadius * cos(315)", "cellSize / 2 + innerRadius * sin(315)" ] ] }, { "polygon": [ [ "cellSize / 2 + edge / 2", "1 * cellSize - edge / 2" ], [ "1 * cellSize + edge * cos(112.5)", "cellSize / 2 + edge * sin(112.5)" ], [ "1 * cellSize", "1 * cellSize" ], [ "1 * cellSize + edge * cos(247.5)", "1 * cellSize + cellSize / 2 + edge * sin(247.5)" ], [ "cellSize / 2 + edge / 2", "1 * cellSize + edge / 2" ] ] }, { "polygon": [ [ "1 * cellSize + edge * cos(157.5)", "cellSize / 2 + edge * sin(157.5)" ], [ "1 * cellSize + innerRadius * cos(135)", "cellSize / 2 + innerRadius * sin(135)" ], [ "1 * cellSize + edge * cos(112.5)", "cellSize / 2 + edge * sin(112.5)" ], [ "cellSize / 2 + edge / 2", "1 * cellSize - edge / 2" ] ] }, { "polygon": [ [ "1 * cellSize", "0" ], [ "1 * cellSize + edge * cos(292.5)", "cellSize / 2 + edge * sin(292.5)" ], [ "1 * cellSize + innerRadius * cos(270)", "cellSize / 2 + innerRadius * sin(270)" ], [ "1 * cellSize + edge * cos(247.5)", "cellSize / 2 + edge * sin(247.5)" ] ] }, { "polygon": [ [ "1 * cellSize + edge * cos(112.5)", "cellSize / 2 + edge * sin(112.5)" ], [ "1 * cellSize + innerRadius * cos(90)", "cellSize / 2 + innerRadius * sin(90)" ], [ "1 * cellSize + edge * cos(67.5)", "cellSize / 2 + edge * sin(67.5)" ], [ "1 * cellSize", "1 * cellSize" ] ] }, { "polygon": [ [ "0", "1 * cellSize" ], [ "edge * cos(67.5)", "cellSize / 2 + edge * sin(67.5)" ], [ "cellSize / 2 - edge / 2", "1 * cellSize - edge / 2" ], [ "cellSize / 2 - edge / 2", "1 * cellSize + edge / 2" ], [ "edge * cos(292.5)", "1 * cellSize + cellSize / 2 + edge * sin(292.5)" ] ] }, { "polygon": [ [ "cellSize / 2 - edge / 2", "edge / 2" ], [ "cellSize / 2 + edge / 2", "edge / 2" ], [ "1 * cellSize + edge * cos(202.5)", "cellSize / 2 + edge * sin(202.5)" ], [ "cellSize / 2", "cellSize / 2" ], [ "edge * cos(337.5)", "cellSize / 2 + edge * sin(337.5)" ] ] }, { "polygon": [ [ "cellSize / 2 - edge / 2", "1 * cellSize - edge / 2" ], [ "cellSize / 2 + edge / 2", "1 * cellSize - edge / 2" ], [ "cellSize / 2 + edge / 2", "1 * cellSize + edge / 2" ], [ "cellSize / 2 - edge / 2", "1 * cellSize + edge / 2" ] ] }, { "polygon": [ [ "innerRadius * cos(45)", "cellSize / 2 + innerRadius * sin(45)" ], [ "edge * cos(22.5)", "cellSize / 2 + edge * sin(22.5)" ], [ "cellSize / 2 - edge / 2", "1 * cellSize - edge / 2" ], [ "edge * cos(67.5)", "cellSize / 2 + edge * sin(67.5)" ] ] }, { "polygon": [ [ "1 * cellSize + edge * cos(202.5)", "cellSize / 2 + edge * sin(202.5)" ], [ "1 * cellSize + innerRadius * cos(180)", "cellSize / 2 + innerRadius * sin(180)" ], [ "1 * cellSize + edge * cos(157.5)", "cellSize / 2 + edge * sin(157.5)" ], [ "cellSize / 2", "cellSize / 2" ] ] }, { "polygon": [ [ "1 * cellSize + innerRadius * cos(180)", "cellSize / 2 + innerRadius * sin(180)" ], [ "1 * cellSize + edge * cos(202.5)", "cellSize / 2 + edge * sin(202.5)" ], [ "1 * cellSize + innerRadius * cos(225)", "cellSize / 2 + innerRadius * sin(225)" ], [ "1 * cellSize + edge * 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sin(157.5)" ] ] }, { "polygon": [ [ "cellSize / 2 + edge / 2", "edge / 2" ], [ "1 * cellSize + edge * cos(247.5)", "cellSize / 2 + edge * sin(247.5)" ], [ "1 * cellSize + innerRadius * cos(225)", "cellSize / 2 + innerRadius * sin(225)" ], [ "1 * cellSize + edge * cos(202.5)", "cellSize / 2 + edge * sin(202.5)" ] ] }, { "polygon": [ [ "innerRadius * cos(0)", "cellSize / 2 + innerRadius * sin(0)" ], [ "edge * cos(337.5)", "cellSize / 2 + edge * sin(337.5)" ], [ "cellSize / 2", "cellSize / 2" ], [ "edge * cos(22.5)", "cellSize / 2 + edge * sin(22.5)" ] ] } ], "lattice": { "a": [ "cellSize", "0" ], "b": [ "0", "cellSize" ] } } ,"offset-strip-basketweave":{ "schema": 1, "id": "offset-strip-basketweave", "name": "Offset strip basketweave", "category": "stone", "parameters": { "length": { "value": 250, "min": 60, "max": 2000, "label": "Paver length" }, "bandWidth": { "value": 35, "min": 5, "max": 400, "label": "Strip course" }, "half": { "expr": "length / 2" }, "block": { "expr": "2 * length" } }, "tiles": [ { "repeat": { "index": "k", "count": "4" }, "rect": ["k * half", "0", "(k + 1) * half", "bandWidth"] }, { "rect": ["0", "bandWidth", "half", "bandWidth + length"] }, { "rect": ["half", "bandWidth", "length", "bandWidth + length"] }, { "rect": ["length", "bandWidth", "block", "bandWidth + half"] }, { "rect": ["length", "bandWidth + half", "block", "bandWidth + length"] } ], "lattice": { "a": ["2 * length", "0"], "b": ["length", "length + bandWidth"] } } ,"ogee-fish-scale":{ "schema": 1, "id": "ogee-fish-scale", "name": "Ogee fish scale", "category": "ceramic", "parameters": { "radius": { "value": 75, "min": 15, "max": 400, "label": "Scale radius" }, "two": { "expr": "2 * radius" }, "three": { "expr": "3 * radius" } }, "tiles": [ { "path": [ { "arc": { "center": ["0", "radius"], "from": ["0", "two"], "to": ["0", "0"], "clockwise": false } }, { "arc": { "center": ["radius", "0"], "from": ["0", "0"], "to": ["radius", "radius"], "clockwise": true } }, { "arc": { "center": 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"clockwise": true } }, { "arc": { "center": ["0", "three"], "from": ["radius", "three"], "to": ["0", "two"], "clockwise": true } } ] } ], "lattice": { "a": ["two", "two"], "b": ["two", "-two"] } } ,"open-cell-ceiling":{ "schema": 1, "id": "open-cell-ceiling", "name": "Open cell ceiling", "category": "metal", "parameters": { "cellSize": { "value": 75, "min": 20, "max": 300, "label": "Cell width" }, "wallWidth": { "value": 5, "min": 1, "max": 30, "label": "Blade width" }, "module": { "expr": "cellSize + wallWidth" } }, "tiles": [ { "rect": ["0", "0", "module", "module"], "holes": [ { "rect": ["wallWidth / 2", "wallWidth / 2", "wallWidth / 2 + cellSize", "wallWidth / 2 + cellSize"] } ] } ], "lattice": { "a": ["module", "0"], "b": ["0", "module"] } } ,"opus-romano-plank":{ "schema": 1, "id": "opus-romano-plank", "name": "Opus Romano (plank format)", "category": "wood", "parameters": { "width": { "value": 200, "min": 20, "max": 1000, "label": "Plank width" } }, "tiles": [ { "rect": ["0", "0", "4 * width", "width"] }, { "rect": ["0", "width", "4 * width", "5 * width"] }, { "rect": ["4 * width", "0", "6 * width", "4 * width"] } ], "lattice": { "a": ["6 * width", "-width"], "b": ["4 * width", "4 * width"] } } ,"opus-romano-three-size":{ "schema": 1, "id": "opus-romano-three-size", "name": "Opus Romano (three sizes)", "category": "stone", "parameters": { "moduleSize": { "value": 200, "min": 20, "max": 1000, "label": "Smallest tile side" } }, "tiles": [ { "rect": ["0", "0", "3 * moduleSize", "3 * moduleSize"] }, { "rect": ["3 * moduleSize", "0", "5 * moduleSize", "3 * moduleSize"] }, { "rect": ["0", "3 * moduleSize", "2 * moduleSize", "5 * moduleSize"] } ], "lattice": { "a": ["5 * moduleSize", "-2 * moduleSize"], "b": ["2 * moduleSize", "3 * moduleSize"] } } ,"opus-romano":{ "schema": 1, "id": "opus-romano", "name": "Opus Romano", "category": "stone", "parameters": { "moduleSize": { "value": 200, "min": 20, "max": 1000, "label": "Smallest tile side" } }, "tiles": [ { "rect": ["0", "0", "2 * moduleSize", "2 * moduleSize"] }, { "rect": ["0", "2 * moduleSize", "moduleSize", "4 * moduleSize"] }, { "rect": ["moduleSize", "2 * moduleSize", "4 * moduleSize", "5 * moduleSize"] }, { "rect": ["2 * moduleSize", "moduleSize", "4 * moduleSize", "2 * moduleSize"] }, { "rect": ["4 * moduleSize", "moduleSize", "6 * moduleSize", "4 * moduleSize"] }, { "rect": ["5 * moduleSize", "0", "6 * moduleSize", "moduleSize"] }, { "rect": ["4 * moduleSize", "4 * moduleSize", "5 * moduleSize", "5 * moduleSize"] }, { "rect": ["moduleSize", "5 * moduleSize", "2 * moduleSize", "6 * moduleSize"] }, { "rect": ["2 * moduleSize", "5 * moduleSize", "5 * moduleSize", "7 * moduleSize"] }, { "rect": ["5 * moduleSize", "4 * moduleSize", "7 * moduleSize", "6 * moduleSize"] } ], "lattice": { "a": ["6 * moduleSize", "0"], "b": ["0", "6 * moduleSize"] } } ,"oval-and-bar-panel":{ "schema": 1, "id": "oval-and-bar-panel", "name": "Oval and bar panel", "category": "ceramic", "parameters": { "width": { "value": 144, "min": 40, "max": 200, "label": "Oval width" }, "length": { "value": 530, "min": 370, "max": 1500, "label": "Oval length" }, "bandWidth": { "value": 50, "min": 10, "max": 80, "label": "Bar width" }, "gap": { "value": 316, "min": 50, "max": 1000, "label": "Gap between ovals" }, "offset": { "value": 0, "min": 0, "max": 1, "label": "Column offset (fraction of the repeat)", "unit": "none" }, "radius": { "expr": "width / 2" }, "column": { "expr": "width + 2 * bandWidth" }, "period": { "expr": "length + gap" }, "inset": { "expr": "width / 2 + bandWidth" } }, "tiles": [ { "start": [ "bandWidth", "radius" ], "path": [ { "arc": { "center": [ "bandWidth + radius", "radius" ], "from": [ "bandWidth", "radius" ], "to": [ "bandWidth + width", "radius" ], "clockwise": false } }, { "line": { "to": [ "bandWidth + width", "length - radius" ] } }, { "arc": { "center": [ "bandWidth + radius", "length - radius" ], "from": [ "bandWidth + width", "length - radius" ], "to": [ "bandWidth", "length - radius" ], "clockwise": false } }, { "line": { "to": [ "bandWidth", "radius" ] } } ] }, { "rect": [ "0", "inset", "bandWidth", "length - inset" ] }, { "rect": [ "bandWidth + width", "inset", "column", "length - inset" ] }, { "start": [ "0", "length - inset" ], "path": [ { "line": { "to": [ "bandWidth", "length - inset" ] } }, { "line": { "to": [ "bandWidth", "length - radius" ] } }, { "arc": { "center": [ "bandWidth + radius", "length - radius" ], "from": [ "bandWidth", "length - radius" ], "to": [ "bandWidth + width", "length - radius" ], "clockwise": true } }, { "line": { "to": [ "bandWidth + width", "length - inset" ] } }, { "line": { "to": [ "column", "length - inset" ] } }, { "line": { "to": [ "column", "period + inset" ] } }, { "line": { "to": [ "bandWidth + width", "period + inset" ] } }, { "line": { "to": [ "bandWidth + width", "period + radius" ] } }, { "arc": { "center": [ "bandWidth + radius", "period + radius" ], "from": [ "bandWidth + width", "period 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"name": "Paddle interlock tile", "category": "ceramic", "parameters": { "width": { "value": 165, "min": 30, "max": 1200, "label": "Tile pitch" }, "headWidth": { "expr": "0.7 * width" }, "stemLeft": { "expr": "0.2 * width" }, "stemRight": { "expr": "0.5 * width" }, "domeLow": { "expr": "-0.4 * width" }, "sideRadius": { "expr": "0.5 * width" }, "capRadius": { "expr": "0.25 * width" }, "capCentre": { "expr": "-0.2 * width" }, "rowStep": { "expr": "1.4 * width" }, "shoulder": { "expr": "1.0 * width" }, "stemTop": { "expr": "2.4 * width" } }, "tiles": [ { "start": ["0", "0"], "path": [ { "arc": { "center": ["sideRadius", "0"], "from": ["0", "0"], "to": ["stemLeft", "domeLow"], "clockwise": false } }, { "arc": { "center": ["0.35 * width", "capCentre"], "from": ["stemLeft", "domeLow"], "to": ["stemRight", "domeLow"], "clockwise": false } }, { "arc": { "center": ["stemLeft", "0"], "from": ["stemRight", "domeLow"], "to": ["headWidth", "0"], "clockwise": false } }, { "line": { "to": 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"value": 300, "min": 60, "max": 2000, "label": "Slat side" }, "bandWidth": { "value": 25, "min": 5, "max": 400, "label": "Band width" }, "skew": { "expr": "width" } }, "tiles": [ { "polygon": [["0", "0"], ["width", "skew"], ["width", "skew + length"], ["0", "length"]] }, { "polygon": [["width", "skew"], ["2 * width", "0"], ["2 * width", "length"], ["width", "skew + length"]] }, { "rect": ["2 * width", "0", "2 * width + bandWidth", "length"] } ], "lattice": { "a": ["2 * width + bandWidth", "0"], "b": ["0", "length"] } } ,"parallelogram":{ "schema": 1, "id": "parallelogram", "name": "Parallelogram", "category": "stone", "parameters": { "length": { "value": 300, "min": 30, "max": 2000, "label": "Long side" }, "width": { "value": 200, "min": 20, "max": 2000, "label": "Slanted side" }, "slantX": { "expr": "width / 2" }, "slantY": { "expr": "width * sqrt(3) / 2" } }, "tiles": [ { "polygon": [ [ "0", "0" ], [ "length", "0" ], [ "length + slantX", "slantY" ], [ "slantX", "slantY" ] ] } ], 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"b": ["(-15 - 13 * sqrt(3)) * edge / 5", "(39 + 15 * sqrt(3)) * edge / 5"] } } ,"six-star-two-point-isfahan":{ "schema": 1, "id": "six-star-two-point-isfahan", "name": "Six-star and rhombi", "category": "ceramic", "parameters": { "edge": { "value": 40, "min": 10, "max": 200, "label": "Edge" } }, "tiles": [ { "polygon": [ ["2 * sqrt(3) * edge / 2", "0"], ["sqrt(3) * edge / 2", "edge / 2"], ["sqrt(3) * edge / 2", "3 * edge / 2"], ["0", "2 * edge / 2"], ["-sqrt(3) * edge / 2", "3 * edge / 2"], ["-sqrt(3) * edge / 2", "edge / 2"], ["-2 * sqrt(3) * edge / 2", "0"], ["-sqrt(3) * edge / 2", "-edge / 2"], ["-sqrt(3) * edge / 2", "-3 * edge / 2"], ["0", "-2 * edge / 2"], ["sqrt(3) * edge / 2", "-3 * edge / 2"], ["sqrt(3) * edge / 2", "-edge / 2"] ] }, { "polygon": [ ["0", "4 * edge / 2"], ["sqrt(3) * edge / 2", "3 * edge / 2"], ["0", "2 * edge / 2"], ["-sqrt(3) * edge / 2", "3 * edge / 2"] ] }, { "polygon": [ ["0", "6 * edge / 2"], ["sqrt(3) * edge / 2", "5 * edge / 2"], ["0", "4 * edge / 2"], 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rowStep" ] ] }, { "polygon": [ [ "4 * halfEdge", "2 * rowStep" ], [ "6 * halfEdge", "2 * rowStep" ], [ "5 * halfEdge", "3 * rowStep" ] ] }, { "polygon": [ [ "3 * halfEdge", "3 * rowStep" ], [ "4 * halfEdge", "2 * rowStep" ], [ "5 * halfEdge", "3 * rowStep" ], [ "4 * halfEdge", "4 * rowStep" ] ] }, { "polygon": [ [ "6 * halfEdge", "0" ], [ "8 * halfEdge", "0" ], [ "7 * halfEdge", "rowStep" ] ] }, { "polygon": [ [ "5 * halfEdge", "rowStep" ], [ "7 * halfEdge", "rowStep" ], [ "6 * halfEdge", "2 * rowStep" ] ] }, { "polygon": [ [ "halfEdge", "3 * rowStep" ], [ "3 * halfEdge", "3 * rowStep" ], [ "4 * halfEdge", "4 * rowStep" ], [ "2 * halfEdge", "4 * rowStep" ] ] }, { "polygon": [ [ "halfEdge", "rowStep" ], [ "3 * halfEdge", "rowStep" ], [ "2 * halfEdge", "2 * rowStep" ] ] }, { "polygon": [ [ "2 * halfEdge", "2 * rowStep" ], [ "4 * halfEdge", "2 * rowStep" ], [ "3 * halfEdge", "3 * rowStep" ] ] }, { "polygon": [ [ "4 * halfEdge", "0" ], [ "6 * halfEdge", "0" ], [ "7 * halfEdge", "rowStep" ], [ "5 * halfEdge", "rowStep" ] ] }, { "polygon": [ [ "halfEdge", "3 * rowStep" ], [ "2 * halfEdge", "4 * rowStep" ], [ "0", "4 * rowStep" ] ] }, { "polygon": [ [ "5 * halfEdge", "3 * rowStep" ], [ "7 * halfEdge", "3 * rowStep" ], [ "6 * halfEdge", "4 * rowStep" ], [ "4 * halfEdge", "4 * rowStep" ] ] }, { "polygon": [ [ "7 * halfEdge", "3 * rowStep" ], [ "8 * halfEdge", "4 * rowStep" ], [ "6 * halfEdge", "4 * rowStep" ] ] }, { "polygon": [ [ "0", "0" ], [ "2 * halfEdge", "0" ], [ "halfEdge", "rowStep" ] ] }, { "polygon": [ [ "3 * halfEdge", "rowStep" ], [ "4 * halfEdge", "0" ], [ "5 * halfEdge", "rowStep" ], [ "4 * halfEdge", "2 * rowStep" ] ] }, { "polygon": [ [ "6 * halfEdge", "2 * rowStep" ], [ "7 * halfEdge", "3 * rowStep" ], [ "5 * halfEdge", "3 * rowStep" ] ] }, { "polygon": [ [ "2 * halfEdge", "0" ], [ "4 * halfEdge", "0" ], [ "3 * halfEdge", "rowStep" ], [ "halfEdge", "rowStep" ] ] }, { "polygon": [ [ "3 * halfEdge", "rowStep" ], [ "4 * halfEdge", "2 * rowStep" ], [ "2 * 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rowStep" ] ] }, { "polygon": [ [ "8 * halfEdge", "0" ], [ "10 * halfEdge", "0" ], [ "9 * halfEdge", "rowStep" ] ] }, { "polygon": [ [ "10 * halfEdge", "2 * rowStep" ], [ "12 * halfEdge", "2 * rowStep" ], [ "13 * halfEdge", "3 * rowStep" ], [ "11 * halfEdge", "3 * rowStep" ] ] }, { "polygon": [ [ "7 * halfEdge", "rowStep" ], [ "8 * halfEdge", "2 * rowStep" ], [ "6 * halfEdge", "2 * rowStep" ] ] }, { "polygon": [ [ "11 * halfEdge", "rowStep" ], [ "13 * halfEdge", "rowStep" ], [ "12 * halfEdge", "2 * rowStep" ], [ "10 * halfEdge", "2 * rowStep" ] ] }, { "polygon": [ [ "halfEdge", "rowStep" ], [ "2 * halfEdge", "2 * rowStep" ], [ "0", "2 * rowStep" ] ] }, { "polygon": [ [ "6 * halfEdge", "2 * rowStep" ], [ "8 * halfEdge", "2 * rowStep" ], [ "7 * halfEdge", "3 * rowStep" ] ] }, { "polygon": [ [ "9 * halfEdge", "3 * rowStep" ], [ "10 * halfEdge", "2 * rowStep" ], [ "11 * halfEdge", "3 * rowStep" ], [ "10 * halfEdge", "4 * rowStep" ] ] }, { "polygon": [ [ "0", "0" ], [ "halfEdge", "rowStep" ], [ "-halfEdge", "rowStep" ] ] }, { "polygon": [ [ "8 * halfEdge", "2 * rowStep" ], [ "10 * halfEdge", "2 * rowStep" ], [ "9 * halfEdge", "3 * rowStep" ], [ "7 * halfEdge", "3 * rowStep" ] ] }, { "polygon": [ [ "9 * halfEdge", "3 * rowStep" ], [ "10 * halfEdge", "4 * rowStep" ], [ "8 * halfEdge", "4 * rowStep" ] ] }, { "polygon": [ [ "11 * halfEdge", "3 * rowStep" ], [ "12 * halfEdge", "4 * rowStep" ], [ "10 * halfEdge", "4 * rowStep" ] ] } ], "lattice": { "a": [ "12 * halfEdge", "0" ], "b": [ "0", "4 * rowStep" ] } } ,"snub-hexagonal":{ "schema": 1, "id": "snub-hexagonal", "name": "Snub hexagonal", "category": "ceramic", "parameters": { "edge": {"value": 100, "min": 10, "max": 500, "label": "Edge"}, "rootThree": {"expr": "sqrt(3)"} }, "tiles": [ { "polygon": [ ["edge", "0"], ["edge / 2", "rootThree * edge / 2"], ["-edge / 2", "rootThree * edge / 2"], ["-edge", "0"], ["-edge / 2", "-rootThree * edge / 2"], ["edge / 2", "-rootThree * edge / 2"] ] }, { "polygon": [ ["3 * edge / 2", "rootThree * edge / 2"], ["edge / 2", "rootThree * edge / 2"], ["edge", "0"] ] }, { "polygon": [ ["-edge / 2", "-rootThree * edge / 2"], ["-edge", "0"], ["-3 * edge / 2", "-rootThree * edge / 2"] ] }, { "polygon": [ ["0", "rootThree * edge"], ["-edge / 2", "rootThree * edge / 2"], ["edge / 2", "rootThree * edge / 2"] ] }, { "polygon": [ ["edge / 2", "-rootThree * edge / 2"], ["-edge / 2", "-rootThree * edge / 2"], ["0", "-rootThree * edge"] ] }, { "polygon": [ ["-edge", "0"], ["-3 * edge / 2", "rootThree * edge / 2"], ["-2 * edge", "0"] ] }, { "polygon": [ ["edge", "0"], ["edge / 2", "-rootThree * edge / 2"], ["3 * edge / 2", "-rootThree * edge / 2"] ] }, { "polygon": [ ["-3 * edge / 2", "-rootThree * edge / 2"], ["-edge", "-rootThree * edge"], ["-edge / 2", "-rootThree * edge / 2"] ] }, { "polygon": [ ["-edge", "0"], ["-edge / 2", "rootThree * edge / 2"], ["-3 * edge / 2", "rootThree * edge / 2"] ] } ], "lattice": { "a": ["5 * edge / 2", "rootThree * edge / 2"], "b": ["edge / 2", "3 * 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"triple-weave-and-dot", "name": "Triple weave and dot", "category": "stone", "parameters": { "length": { "value": 250, "min": 60, "max": 2000, "label": "Paver length" }, "width": { "value": 50, "min": 10, "max": 600, "label": "Paver width" }, "block": { "expr": "3 * width" } }, "tiles": [ { "repeat": { "index": "k", "count": "3" }, "rect": ["0", "k * width", "length", "(k + 1) * width"] }, { "repeat": { "index": "k", "count": "9" }, "rect": ["length + floor(k / 3) * width", "(k - 3 * floor(k / 3)) * width", "length + (floor(k / 3) + 1) * width", "(k - 3 * floor(k / 3) + 1) * width"] }, { "repeat": { "index": "k", "count": "3" }, "rect": ["length + k * width", "block", "length + (k + 1) * width", "block + length"] }, { "rect": ["0", "block", "length", "block + length"] } ], "lattice": { "a": ["length + block", "0"], "b": ["0", "length + block"] } } ,"truncated-hexagonal":{ "schema": 1, "id": "truncated-hexagonal", "name": "Truncated hexagonal", "category": "ceramic", "parameters": { "edge": {"value": 50, "min": 10, "max": 500, "label": "Edge"}, "rootThree": {"expr": "sqrt(3)"} }, "tiles": [ { "polygon": [ ["edge * (2 + rootThree) / 2", "edge / 2"], ["edge * (1 + rootThree) / 2", "edge * (1 + rootThree) / 2"], ["edge / 2", "edge * (2 + rootThree) / 2"], ["-edge / 2", "edge * (2 + rootThree) / 2"], ["edge * (-1 - rootThree) / 2", "edge * (1 + rootThree) / 2"], ["edge * (-2 - rootThree) / 2", "edge / 2"], ["edge * (-2 - rootThree) / 2", "-edge / 2"], ["edge * (-1 - rootThree) / 2", "edge * (-1 - rootThree) / 2"], ["-edge / 2", "edge * (-2 - rootThree) / 2"], ["edge / 2", "edge * (-2 - rootThree) / 2"], ["edge * (1 + rootThree) / 2", "edge * (-1 - rootThree) / 2"], ["edge * (2 + rootThree) / 2", "-edge / 2"] ] }, { "polygon": [ ["edge * (-1 - rootThree) / 2", "edge * (1 + rootThree) / 2"], ["edge * (-3 - rootThree) / 2", "edge * (1 + rootThree) / 2"], ["edge * (-2 - rootThree) / 2", "edge / 2"] ] }, { "polygon": [ ["edge * (-2 - rootThree) / 2", "-edge / 2"], ["edge * (-3 - rootThree) / 2", "edge * (-1 - rootThree) / 2"], ["edge * (-1 - rootThree) / 2", "edge * (-1 - rootThree) / 2"] ] } ], "lattice": { "a": ["edge * (2 + rootThree)", "0"], "b": ["edge * (2 + rootThree) / 2", "edge * (3 + 2 * rootThree) / 2"] } } ,"truncated-trihexagonal":{ "schema": 1, "id": "truncated-trihexagonal", "name": "Truncated trihexagonal", "category": "ceramic", "parameters": { "edge": {"value": 50, "min": 10, "max": 500, "label": "Edge"}, "rootThree": {"expr": "sqrt(3)"} }, "tiles": [ { "polygon": [ ["edge * (2 + rootThree) / 2", "edge / 2"], ["edge * (1 + rootThree) / 2", "edge * (1 + rootThree) / 2"], ["edge / 2", "edge * (2 + rootThree) / 2"], ["-edge / 2", "edge * (2 + rootThree) / 2"], ["edge * (-1 - rootThree) / 2", "edge * (1 + rootThree) / 2"], ["edge * (-2 - rootThree) / 2", "edge / 2"], ["edge * (-2 - rootThree) / 2", "-edge / 2"], ["edge * (-1 - rootThree) / 2", "edge * (-1 - rootThree) / 2"], ["-edge / 2", "edge * (-2 - rootThree) / 2"], ["edge / 2", "edge * (-2 - rootThree) / 2"], ["edge * (1 + rootThree) / 2", "edge * (-1 - rootThree) / 2"], ["edge * (2 + rootThree) / 2", "-edge / 2"] ] }, { "polygon": [ ["edge * (-2 - rootThree) / 2", "edge / 2"], ["edge * (-1 - rootThree) / 2", "edge * (1 + rootThree) / 2"], ["edge * (-2 - rootThree) / 2", "edge * (1 + 2 * rootThree) / 2"], ["edge * (-4 - rootThree) / 2", "edge * (1 + 2 * rootThree) / 2"], ["edge * (-5 - rootThree) / 2", "edge * (1 + rootThree) / 2"], ["edge * (-4 - rootThree) / 2", "edge / 2"] ] }, { "polygon": [ ["-edge / 2", "edge * (-2 - rootThree) / 2"], ["edge * (-1 - rootThree) / 2", "edge * (-1 - rootThree) / 2"], ["edge * (-2 - rootThree) / 2", "edge * (-1 - 2 * rootThree) / 2"], ["-edge", "edge * (-1 - rootThree)"] ] }, { "polygon": [ ["edge * (-1 - rootThree) / 2", "edge * (-1 - rootThree) / 2"], ["edge * (-2 - rootThree) / 2", "-edge / 2"], ["edge * (-4 - rootThree) / 2", "-edge / 2"], ["edge * (-5 - rootThree) / 2", "edge * (-1 - rootThree) / 2"], ["edge * (-4 - rootThree) / 2", "edge * (-1 - 2 * rootThree) / 2"], ["edge * (-2 - rootThree) / 2", "edge * (-1 - 2 * rootThree) / 2"] ] }, { "polygon": [ ["-edge", "edge * (1 + rootThree)"], ["edge * (-2 - rootThree) / 2", "edge * (1 + 2 * rootThree) / 2"], ["edge * (-1 - rootThree) / 2", "edge * (1 + rootThree) / 2"], ["-edge / 2", "edge * (2 + rootThree) / 2"] ] }, { "polygon": [ ["edge * (-4 - rootThree) / 2", "edge / 2"], ["edge * (-4 - rootThree) / 2", "-edge / 2"], ["edge * (-2 - rootThree) / 2", "-edge / 2"], ["edge * (-2 - rootThree) / 2", "edge / 2"] ] } ], "lattice": { "a": ["edge * (3 + rootThree)", "0"], "b": ["edge * (3 + rootThree) / 2", "edge * (3 + 3 * rootThree) / 2"] } } ,"tumbling-blocks":{ "schema": 1, "id": "tumbling-blocks", "name": "Tumbling blocks", "category": "ceramic", "parameters": { "edge": { "value": 175, "min": 20, "max": 600, "label": "Rhombus side" } }, "tiles": [ { "polygon": [["0", "0"], ["edge", "0"], ["edge / 2", "sqrt(3) * edge / 2"], ["-edge / 2", "sqrt(3) * edge / 2"]] }, { "polygon": [["0", "0"], ["-edge / 2", "sqrt(3) * edge / 2"], ["-edge", "0"], ["-edge / 2", "-sqrt(3) * edge / 2"]] }, { "polygon": [["0", "0"], ["-edge / 2", "-sqrt(3) * edge / 2"], ["edge / 2", "-sqrt(3) * edge / 2"], ["edge", "0"]] } ], "lattice": { "a": ["3 * edge / 2", "sqrt(3) * edge / 2"], "b": ["0", "sqrt(3) * edge"] } } ,"twelve-star-fountain-fez":{ "schema": 1, "id": "twelve-star-fountain-fez", "name": "Twelve-point star fountain pattern", "category": "ceramic", "parameters": { "edge": { "value": 30, "min": 10, "max": 100, "label": "Star edge" } }, "tiles": [ { "polygon": [ ["(1 + sqrt(3)) * edge / 2", "(-3 - sqrt(3)) * edge / 2"], ["(1 + sqrt(3)) * edge / 2", "(-1 - sqrt(3)) * edge / 2"], ["(3 + sqrt(3)) * edge / 2", "(-1 - sqrt(3)) * edge / 2"], ["(2 + sqrt(3)) * edge / 2", "-1 * edge / 2"], ["(1 + sqrt(3)) * edge", "0"], ["(2 + sqrt(3)) * edge / 2", "1 * edge / 2"], ["(3 + sqrt(3)) * edge / 2", "(1 + sqrt(3)) * edge / 2"], ["(1 + sqrt(3)) * edge / 2", "(1 + sqrt(3)) * edge / 2"], ["(1 + sqrt(3)) * edge / 2", "(3 + sqrt(3)) * edge / 2"], ["1 * edge / 2", "(2 + sqrt(3)) * edge / 2"], ["0", "(1 + sqrt(3)) * edge"], ["-1 * edge / 2", "(2 + sqrt(3)) * edge / 2"], ["(-1 - sqrt(3)) * edge / 2", "(3 + sqrt(3)) * edge / 2"], ["(-1 - sqrt(3)) * edge / 2", "(1 + sqrt(3)) * edge / 2"], ["(-3 - sqrt(3)) * edge / 2", "(1 + sqrt(3)) * edge / 2"], ["(-2 - sqrt(3)) * edge / 2", "1 * edge / 2"], ["(-1 - sqrt(3)) * edge", "0"], ["(-2 - sqrt(3)) * edge / 2", "-1 * edge / 2"], ["(-3 - sqrt(3)) * edge / 2", "(-1 - sqrt(3)) * edge / 2"], ["(-1 - sqrt(3)) * edge / 2", "(-1 - sqrt(3)) * edge / 2"], ["(-1 - sqrt(3)) * edge / 2", "(-3 - sqrt(3)) * edge / 2"], ["-1 * edge / 2", "(-2 - sqrt(3)) * edge / 2"], ["0", "(-1 - sqrt(3)) * edge"], ["1 * edge / 2", "(-2 - sqrt(3)) * edge / 2"] ] }, { "polygon": [ ["0", "(7 + 3 * sqrt(3)) * edge"], ["1 * edge / 2", "(14 + 7 * sqrt(3)) * edge / 2"], ["(1 + sqrt(3)) * edge / 2", "(13 + 7 * sqrt(3)) * edge / 2"], ["(1 + sqrt(3)) * edge / 2", "(15 + 7 * sqrt(3)) * edge / 2"], ["(3 + sqrt(3)) * edge / 2", "(15 + 7 * sqrt(3)) * edge / 2"], ["(2 + sqrt(3)) * edge / 2", "(15 + 8 * sqrt(3)) * edge / 2"], ["(1 + sqrt(3)) * edge", "(8 + 4 * sqrt(3)) * edge"], ["(2 + sqrt(3)) * edge / 2", "(17 + 8 * sqrt(3)) * edge / 2"], ["(3 + sqrt(3)) * edge / 2", "(17 + 9 * sqrt(3)) * edge / 2"], ["(1 + sqrt(3)) * edge / 2", "(17 + 9 * sqrt(3)) * edge / 2"], ["(1 + sqrt(3)) * edge / 2", "(19 + 9 * sqrt(3)) * edge / 2"], ["1 * edge / 2", "(18 + 9 * sqrt(3)) * edge / 2"], ["0", "(9 + 5 * sqrt(3)) * edge"], ["-1 * edge / 2", "(18 + 9 * sqrt(3)) * edge / 2"], ["(-1 - sqrt(3)) * edge / 2", "(19 + 9 * sqrt(3)) * edge / 2"], ["(-1 - sqrt(3)) * edge / 2", "(17 + 9 * sqrt(3)) * edge / 2"], ["(-3 - sqrt(3)) * edge / 2", "(17 + 9 * sqrt(3)) * edge / 2"], ["(-2 - sqrt(3)) * edge / 2", "(17 + 8 * sqrt(3)) * edge / 2"], ["(-1 - sqrt(3)) * edge", "(8 + 4 * sqrt(3)) * edge"], ["(-2 - sqrt(3)) * edge / 2", "(15 + 8 * sqrt(3)) * edge / 2"], ["(-3 - sqrt(3)) * edge / 2", "(15 + 7 * sqrt(3)) * edge / 2"], ["(-1 - sqrt(3)) * edge / 2", "(15 + 7 * sqrt(3)) * edge / 2"], ["(-1 - sqrt(3)) * edge / 2", "(13 + 7 * sqrt(3)) * edge / 2"], ["-1 * edge / 2", "(14 + 7 * sqrt(3)) * edge / 2"] ] }, { "polygon": [ ["(7 + 3 * sqrt(3)) * edge", "0"], ["(14 + 7 * sqrt(3)) * edge / 2", "-1 * edge / 2"], ["(13 + 7 * sqrt(3)) * edge / 2", "(-1 - sqrt(3)) * edge / 2"], ["(15 + 7 * sqrt(3)) * edge / 2", "(-1 - sqrt(3)) * edge / 2"], ["(15 + 7 * sqrt(3)) * edge / 2", "(-3 - sqrt(3)) * edge / 2"], ["(15 + 8 * sqrt(3)) * edge / 2", "(-2 - sqrt(3)) * edge / 2"], ["(8 + 4 * sqrt(3)) * edge", "(-1 - sqrt(3)) * edge"], ["(17 + 8 * sqrt(3)) * edge / 2", "(-2 - sqrt(3)) * edge / 2"], ["(17 + 9 * sqrt(3)) * edge / 2", "(-3 - sqrt(3)) * edge / 2"], ["(17 + 9 * sqrt(3)) * edge / 2", "(-1 - sqrt(3)) * edge / 2"], ["(19 + 9 * sqrt(3)) * edge / 2", "(-1 - sqrt(3)) * edge / 2"], ["(18 + 9 * sqrt(3)) * edge / 2", "-1 * edge / 2"], ["(9 + 5 * sqrt(3)) * edge", "0"], ["(18 + 9 * sqrt(3)) * edge / 2", "1 * edge / 2"], ["(19 + 9 * sqrt(3)) * edge / 2", "(1 + sqrt(3)) * edge / 2"], ["(17 + 9 * sqrt(3)) * edge / 2", "(1 + sqrt(3)) * edge / 2"], ["(17 + 9 * sqrt(3)) * edge / 2", "(3 + sqrt(3)) * edge / 2"], ["(17 + 8 * sqrt(3)) * edge / 2", "(2 + sqrt(3)) * edge / 2"], ["(8 + 4 * sqrt(3)) * edge", "(1 + sqrt(3)) * edge"], ["(15 + 8 * sqrt(3)) * edge / 2", "(2 + sqrt(3)) * edge / 2"], ["(15 + 7 * sqrt(3)) * edge / 2", "(3 + sqrt(3)) * edge / 2"], ["(15 + 7 * sqrt(3)) * edge / 2", "(1 + sqrt(3)) * edge / 2"], ["(13 + 7 * sqrt(3)) * edge / 2", "(1 + sqrt(3)) * edge / 2"], ["(14 + 7 * sqrt(3)) * edge / 2", "1 * edge / 2"] ] }, { "polygon": [ ["(16 - 2 * sqrt(2) + 8 * sqrt(3) - sqrt(6)) * edge / 2", "(16 - sqrt(2) + 8 * sqrt(3)) * edge / 2"], ["(32 - 3 * sqrt(2) + 16 * sqrt(3) - sqrt(6)) * edge / 4", "(32 - sqrt(2) + 16 * sqrt(3) - sqrt(6)) * edge / 4"], ["(16 - sqrt(2) + 8 * sqrt(3) - sqrt(6)) * edge / 2", "(16 - sqrt(2) + 8 * sqrt(3) - sqrt(6)) * edge / 2"], ["(32 - sqrt(2) + 16 * sqrt(3) - sqrt(6)) * edge / 4", "(32 - 3 * sqrt(2) + 16 * sqrt(3) - sqrt(6)) * edge / 4"], ["(16 - sqrt(2) + 8 * sqrt(3)) * edge / 2", "(16 - 2 * sqrt(2) + 8 * sqrt(3) - sqrt(6)) * edge / 2"], ["(8 + 4 * sqrt(3)) * edge", "(16 - sqrt(2) + 8 * sqrt(3) - sqrt(6)) * edge / 2"], ["(16 + sqrt(2) + 8 * sqrt(3)) * edge / 2", "(16 - 2 * sqrt(2) + 8 * sqrt(3) - sqrt(6)) * edge / 2"], ["(32 + sqrt(2) + 16 * sqrt(3) + sqrt(6)) * edge / 4", "(32 - 3 * sqrt(2) + 16 * sqrt(3) - sqrt(6)) * edge / 4"], ["(16 + sqrt(2) + 8 * sqrt(3) + sqrt(6)) * edge / 2", "(16 - sqrt(2) + 8 * sqrt(3) - sqrt(6)) * edge / 2"], ["(32 + 3 * sqrt(2) + 16 * sqrt(3) + sqrt(6)) * edge / 4", "(32 - sqrt(2) + 16 * sqrt(3) - sqrt(6)) * edge / 4"], ["(16 + 2 * sqrt(2) + 8 * sqrt(3) + sqrt(6)) * edge / 2", "(16 - sqrt(2) + 8 * sqrt(3)) * edge / 2"], ["(16 + sqrt(2) + 8 * sqrt(3) + sqrt(6)) * edge / 2", "(8 + 4 * sqrt(3)) * edge"], ["(16 + 2 * sqrt(2) + 8 * sqrt(3) + sqrt(6)) * edge / 2", "(16 + sqrt(2) + 8 * sqrt(3)) * edge / 2"], ["(32 + 3 * sqrt(2) + 16 * sqrt(3) + sqrt(6)) * edge / 4", "(32 + sqrt(2) + 16 * sqrt(3) + sqrt(6)) * edge / 4"], ["(16 + sqrt(2) + 8 * sqrt(3) + sqrt(6)) * edge / 2", "(16 + sqrt(2) + 8 * sqrt(3) + sqrt(6)) * edge / 2"], ["(32 + sqrt(2) + 16 * sqrt(3) + sqrt(6)) * edge / 4", "(32 + 3 * sqrt(2) + 16 * sqrt(3) + sqrt(6)) * edge / 4"], ["(16 + sqrt(2) + 8 * sqrt(3)) * edge / 2", "(16 + 2 * sqrt(2) + 8 * sqrt(3) + sqrt(6)) * edge / 2"], ["(8 + 4 * sqrt(3)) * edge", "(16 + sqrt(2) + 8 * sqrt(3) + sqrt(6)) * edge / 2"], ["(16 - sqrt(2) + 8 * sqrt(3)) * edge / 2", "(16 + 2 * sqrt(2) + 8 * sqrt(3) + sqrt(6)) * edge / 2"], ["(32 - sqrt(2) + 16 * sqrt(3) - sqrt(6)) * edge / 4", "(32 + 3 * sqrt(2) + 16 * sqrt(3) + sqrt(6)) * edge / 4"], ["(16 - sqrt(2) + 8 * sqrt(3) - sqrt(6)) * edge / 2", "(16 + sqrt(2) + 8 * sqrt(3) + sqrt(6)) * edge / 2"], ["(32 - 3 * sqrt(2) + 16 * sqrt(3) - sqrt(6)) * edge / 4", "(32 + sqrt(2) + 16 * sqrt(3) + sqrt(6)) * edge / 4"], ["(16 - 2 * sqrt(2) + 8 * sqrt(3) - sqrt(6)) * edge / 2", "(16 + sqrt(2) + 8 * sqrt(3)) * edge / 2"], ["(16 - sqrt(2) + 8 * sqrt(3) - sqrt(6)) * edge / 2", "(8 + 4 * sqrt(3)) * edge"] ] }, { "polygon": [ ["(-4 - 2 * sqrt(3)) * edge", "(5 + 3 * sqrt(3)) * edge"], ["(-5 - 2 * sqrt(3)) * edge", "(6 + 3 * sqrt(3)) * edge"], ["(-14 + 2 * sqrt(2) - 6 * sqrt(3) + sqrt(6)) * edge / 2", "(14 - sqrt(2) + 6 * sqrt(3)) * edge / 2"], ["(-16 + 3 * sqrt(2) - 8 * sqrt(3) + 2 * sqrt(6)) * edge / 2", "(16 - 2 * sqrt(2) + 8 * sqrt(3) - sqrt(6)) * edge / 2"], ["(-16 + sqrt(2) - 8 * sqrt(3) + sqrt(6)) * edge / 2", "(16 - sqrt(2) + 8 * sqrt(3) - sqrt(6)) * edge / 2"], ["(-16 + 2 * sqrt(2) - 8 * sqrt(3) + sqrt(6)) * edge / 2", "(16 - 3 * sqrt(2) + 8 * sqrt(3) - 2 * sqrt(6)) * edge / 2"], ["(-14 + sqrt(2) - 6 * sqrt(3)) * edge / 2", "(14 - 2 * sqrt(2) + 6 * sqrt(3) - sqrt(6)) * edge / 2"], ["(-6 - 3 * sqrt(3)) * edge", "(5 + 2 * sqrt(3)) * edge"], ["(-5 - 3 * sqrt(3)) * edge", "(4 + 2 * sqrt(3)) * edge"], ["(-5 - 2 * sqrt(3)) * edge", "(5 + 2 * sqrt(3)) * edge"] ] }, { "polygon": [ ["(-4 - 2 * sqrt(3)) * edge", "(-5 - 3 * sqrt(3)) * edge"], ["(-5 - 2 * sqrt(3)) * edge", "(-5 - 2 * sqrt(3)) * edge"], ["(-5 - 3 * sqrt(3)) * edge", "(-4 - 2 * sqrt(3)) * edge"], ["(-6 - 3 * sqrt(3)) * edge", "(-5 - 2 * sqrt(3)) * edge"], ["(-14 + sqrt(2) - 6 * sqrt(3)) * edge / 2", "(-14 + 2 * sqrt(2) - 6 * sqrt(3) + sqrt(6)) * edge / 2"], ["(-16 + 2 * sqrt(2) - 8 * sqrt(3) + sqrt(6)) * edge / 2", "(-16 + 3 * sqrt(2) - 8 * sqrt(3) + 2 * sqrt(6)) * edge / 2"], ["(-16 + sqrt(2) - 8 * sqrt(3) + sqrt(6)) * edge / 2", "(-16 + sqrt(2) - 8 * sqrt(3) + sqrt(6)) * edge / 2"], ["(-16 + 3 * sqrt(2) - 8 * sqrt(3) + 2 * sqrt(6)) * edge / 2", "(-16 + 2 * sqrt(2) - 8 * sqrt(3) + sqrt(6)) * edge / 2"], ["(-14 + 2 * sqrt(2) - 6 * sqrt(3) + sqrt(6)) * edge / 2", "(-14 + sqrt(2) - 6 * sqrt(3)) * edge / 2"], ["(-5 - 2 * sqrt(3)) * edge", "(-6 - 3 * sqrt(3)) * edge"] ] }, { "polygon": [ ["(4 + 2 * sqrt(3)) * edge", "(-5 - 3 * sqrt(3)) * edge"], ["(5 + 2 * sqrt(3)) * edge", "(-6 - 3 * sqrt(3)) * edge"], ["(14 - 2 * sqrt(2) + 6 * sqrt(3) - sqrt(6)) * edge / 2", "(-14 + sqrt(2) - 6 * sqrt(3)) * edge / 2"], ["(16 - 3 * sqrt(2) + 8 * sqrt(3) - 2 * sqrt(6)) * edge / 2", "(-16 + 2 * sqrt(2) - 8 * sqrt(3) + sqrt(6)) * edge / 2"], ["(16 - sqrt(2) + 8 * sqrt(3) - sqrt(6)) * edge / 2", "(-16 + sqrt(2) - 8 * sqrt(3) + sqrt(6)) * edge / 2"], ["(16 - 2 * sqrt(2) + 8 * sqrt(3) - sqrt(6)) * edge / 2", "(-16 + 3 * sqrt(2) - 8 * sqrt(3) + 2 * sqrt(6)) * edge / 2"], ["(14 - sqrt(2) + 6 * sqrt(3)) * edge / 2", "(-14 + 2 * sqrt(2) - 6 * sqrt(3) + sqrt(6)) * edge / 2"], ["(6 + 3 * sqrt(3)) * edge", "(-5 - 2 * sqrt(3)) * edge"], ["(5 + 3 * sqrt(3)) * edge", "(-4 - 2 * sqrt(3)) * edge"], ["(5 + 2 * sqrt(3)) * edge", "(-5 - 2 * sqrt(3)) * edge"] ] }, { "polygon": [ ["(4 + 2 * sqrt(3)) * edge", "(5 + 3 * sqrt(3)) * edge"], ["(5 + 2 * sqrt(3)) * edge", "(5 + 2 * sqrt(3)) * edge"], ["(5 + 3 * sqrt(3)) * edge", "(4 + 2 * sqrt(3)) * edge"], ["(6 + 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width / 3"], ["-endBulge", "width / 3"] ] } ], "lattice": { "a": ["length", "0"], "b": ["length / 2", "width"] } } ,"zigzag-parallelogram":{ "schema": 1, "id": "zigzag-parallelogram", "name": "Zigzag parallelogram", "category": "stone", "parameters": { "moduleSize": { "value": 60, "min": 10, "max": 400, "label": "Module side" } }, "tiles": [ { "polygon": [ [ "0", "6 * moduleSize" ], [ "2 * moduleSize", "9 * moduleSize" ], [ "0", "12 * moduleSize" ] ] }, { "polygon": [ [ "2 * moduleSize", "9 * moduleSize" ], [ "6 * moduleSize", "9 * moduleSize" ], [ "4 * moduleSize", "12 * moduleSize" ], [ "0", "12 * moduleSize" ] ] }, { "polygon": [ [ "6 * moduleSize", "9 * moduleSize" ], [ "8 * moduleSize", "12 * moduleSize" ], [ "4 * moduleSize", "12 * moduleSize" ] ] }, { "polygon": [ [ "6 * moduleSize", "9 * moduleSize" ], [ "10 * moduleSize", "9 * moduleSize" ], [ "12 * moduleSize", "12 * moduleSize" ], [ "8 * moduleSize", "12 * moduleSize" ] ] }, { "polygon": [ [ "10 * moduleSize", "9 * 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] ] }, { "polygon": [ [ "6 * moduleSize", "3 * moduleSize" ], [ "10 * moduleSize", "3 * moduleSize" ], [ "12 * moduleSize", "6 * moduleSize" ], [ "8 * moduleSize", "6 * moduleSize" ] ] }, { "polygon": [ [ "10 * moduleSize", "3 * moduleSize" ], [ "12 * moduleSize", "0" ], [ "12 * moduleSize", "6 * moduleSize" ] ] }, { "polygon": [ [ "0", "0" ], [ "4 * moduleSize", "0" ], [ "6 * moduleSize", "3 * moduleSize" ], [ "2 * moduleSize", "3 * moduleSize" ] ] }, { "polygon": [ [ "8 * moduleSize", "0" ], [ "12 * moduleSize", "0" ], [ "10 * moduleSize", "3 * moduleSize" ], [ "6 * moduleSize", "3 * moduleSize" ] ] } ], "lattice": { "a": [ "12 * moduleSize", "0" ], "b": [ "0", "12 * moduleSize" ] } },"zigzag-split":{ "schema": 1, "id": "zigzag-split", "name": "Zigzag split panel", "category": "ceramic", "parameters": { "moduleSize": { "value": 50, "min": 15, "max": 400, "label": "Module side" } }, "tiles": [ { "polygon": [["0", "0"], ["2 * moduleSize", "moduleSize"], ["2 * moduleSize", "4 * moduleSize"], ["0", "3 * moduleSize"]] }, { "polygon": [["0", "3 * moduleSize"], ["2 * moduleSize", "4 * moduleSize"], ["0", "4 * moduleSize"]] }, { "polygon": [["4 * moduleSize", "3 * moduleSize"], ["4 * moduleSize", "4 * moduleSize"], ["2 * moduleSize", "4 * moduleSize"]] }, { "polygon": [["2 * moduleSize", "moduleSize"], ["4 * moduleSize", "0"], ["4 * moduleSize", "3 * moduleSize"], ["2 * moduleSize", "4 * moduleSize"]] }, { "polygon": [["4 * moduleSize", "0"], ["2 * moduleSize", "moduleSize"], ["0", "0"]] } ], "lattice": { "a": ["4 * moduleSize", "0"], "b": ["0", "4 * moduleSize"] } } },"sections":{"angled-sawtooth":{ "schema": 1, "id": "angled-sawtooth", "name": "Angled sawtooth", "group": "metal", "source": "A saw tooth whose crest sits a quarter of the period in: a short steep flank and a long shallow one. architextures.org/create, the material panel's Surface Profile list, opened 2026-10-20: the name and the depth-to-period proportion read off its thumbnail (one period drawn 52 px wide, so the proportion is read to about 1/52) (0.44).", "periodMm": 100, "depthMm": 44, "profile": { "start": [ "0", "0" ], "section": [ { "line": { "to": [ "0.25 * period", "depth" ] } }, { "line": { "to": [ "period", "0" ] } } ] } } ,"angled-trapezoid":{ "schema": 1, "id": "angled-trapezoid", "name": "Angled trapezoid", "group": "metal", "source": "An asymmetric rib: a long flank climbing over two thirds of the period, a short one back down over an eighth, then a flat pan. architextures.org/create, the material panel's Surface Profile list, opened 2026-10-20: the name and the depth-to-period proportion read off its thumbnail (one period drawn 52 px wide, so the proportion is read to about 1/52) (0.33).", "periodMm": 100, "depthMm": 33, "profile": { "start": [ "0", "0" ], "section": [ { "line": { "to": [ "0.66 * period", "depth" ] } }, { "line": { "to": [ "0.78 * period", "0" ] } }, { "line": { "to": [ "period", "0" ] } } ] } } ,"curved-trapezoid":{ "schema": 1, "id": "curved-trapezoid", "name": "Curved trapezoid", "group": "metal", "source": "A trapezoidal rib whose flanks are S curves horizontal at both ends (a cubic Bezier over a run of `depth`), so the pan and the crown meet it without a kink: pan, flank, crown 0.44 of the period, flank, pan. architextures.org/create, the material panel's Surface Profile list, opened 2026-10-20: the name and the depth-to-period proportion read off its thumbnail (one period drawn 52 px wide, so the proportion is read to about 1/52) (0.14).", "periodMm": 100, "depthMm": 14, "profile": { "start": [ "0", "0" ], "section": [ { "line": { "to": [ "0.14 * period", "0" ] } }, { "bezier": { "c1": [ "0.14 * period + depth / 2", "0" ], "c2": [ "0.14 * period + depth / 2", "depth" ], "to": [ "0.14 * period + depth", "depth" ] } }, { "line": { "to": [ "0.86 * period - depth", "depth" ] } }, { "bezier": { "c1": [ "0.86 * period - depth / 2", "depth" ], "c2": [ "0.86 * period - depth / 2", "0" ], "to": [ "0.86 * period", "0" ] } }, { "line": { "to": [ "period", "0" ] } } ] } } ,"deep-incline-wave":{ "schema": 1, "id": "deep-incline-wave", "name": "Deep incline wave", "group": "metal", "source": "A long S curve climbing to a crest at 0.85 of the period, then a straight fall to the period line. architextures.org/create, the material panel's Surface Profile list, opened 2026-10-20: the name and the depth-to-period proportion read off its thumbnail (one period drawn 52 px wide, so the proportion is read to about 1/52) (0.22).", "periodMm": 100, "depthMm": 22, "profile": { "start": [ "0", "0" ], "section": [ { "bezier": { "c1": [ "0.4 * period", "0" ], "c2": [ "0.6 * period", "depth" ], "to": [ "0.85 * period", "depth" ] } }, { "line": { "to": [ "period", "0" ] } } ] } } ,"double-corrugated":{ "schema": 1, "id": "double-corrugated", "name": "Double corrugated", "group": "metal", "source": "Two round corrugations per period of unequal depth: a deep one over 0.6 of the period and a shallow one of half the depth over the rest, each an S curve horizontal at its crest and its trough. architextures.org/create, the material panel's Surface Profile list, opened 2026-10-20: the name and the depth-to-period proportion read off its thumbnail (one period drawn 52 px wide, so the proportion is read to about 1/52) (0.27, its crest split by a shallower second wave).", "periodMm": 100, "depthMm": 27, "profile": { "start": [ "0", "0" ], "section": [ { "bezier": { "c1": [ "0.15 * period", "0" ], "c2": [ "0.15 * period", "depth" ], "to": [ "0.3 * period", "depth" ] } }, { "bezier": { "c1": [ "0.45 * period", "depth" ], "c2": [ "0.45 * period", "0" ], "to": [ "0.6 * period", "0" ] } }, { "bezier": { "c1": [ "0.7 * period", "0" ], "c2": [ "0.7 * period", "0.5 * depth" ], "to": [ "0.8 * period", "0.5 * depth" ] } }, { "bezier": { "c1": [ "0.9 * period", "0.5 * depth" ], "c2": [ "0.9 * period", "0" ], "to": [ "period", "0" ] } } ] } } ,"double-shadow-gap-142":{ "schema": 1, "id": "double-shadow-gap-142", "name": "Double shadow gap 142", "group": "wood", "source": "The shadow gap board with a second recess of the same size at mid cover, so one board reads as two. The number in the name is the period, mm: the cover one board takes on the wall. 92 and 142 are sourced ThermoWood cladding widths (Beesley & Fildes 20 x 92 mm ThermoWood TIGA rainscreen; Lunawood Luna Bevel HF 26 x 142, 121 mm coverage; both opened 2026-10-20), 66 and 117 are the steps of the same series as Architextures lists them. architextures.org/create, the material panel's Surface Profile list, opened 2026-10-20: the name and the depth-to-period proportion read off its thumbnail (one period drawn 52 px wide, so the proportion is read to about 1/52)", "periodMm": 142, "depthMm": 10, "profile": { "start": [ "0", "0" ], "section": [ { "line": { "to": [ "depth", "0" ] } }, { "line": { "to": [ "depth", "depth" ] } }, { "line": { "to": [ "0.5 * period - depth", "depth" ] } }, { "line": { "to": [ "0.5 * period - depth", "0" ] } }, { "line": { "to": [ "0.5 * period", "0" ] } }, { "line": { "to": [ "0.5 * period", "depth" ] } }, { "line": { "to": [ "period", "depth" ] } } ] } } ,"double-trapezoid":{ "schema": 1, "id": "double-trapezoid", "name": "Double trapezoid", "group": "metal", "source": "Two identical trapezoidal ribs per period (flank 0.05, crown 0.15, flank 0.05 of the period each), the pans between them a quarter of the period. architextures.org/create, the material panel's Surface Profile list, opened 2026-10-20: the name and the depth-to-period proportion read off its thumbnail (one period drawn 52 px wide, so the proportion is read to about 1/52) (0.16).", "periodMm": 100, "depthMm": 16, "profile": { "start": [ "0", "0" ], "section": [ { "line": { "to": [ "0.125 * period", "0" ] } }, { "line": { "to": [ "0.175 * period", "depth" ] } }, { "line": { "to": [ "0.325 * period", "depth" ] } }, { "line": { "to": [ "0.375 * period", "0" ] } }, { "line": { "to": [ "0.625 * period", "0" ] } }, { "line": { "to": [ "0.675 * period", "depth" ] } }, { "line": { "to": [ "0.825 * period", "depth" ] } }, { "line": { "to": [ "0.875 * period", "0" ] } }, { "line": { "to": [ "period", "0" ] } } ] } } ,"even-trapezoid":{ "schema": 1, "id": "even-trapezoid", "name": "Even trapezoid", "group": "metal", "source": "A trapezoidal rib in equal quarters: flank, crown, flank, pan. architextures.org/create, the material panel's Surface Profile list, opened 2026-10-20: the name and the depth-to-period proportion read off its thumbnail (one period drawn 52 px wide, so the proportion is read to about 1/52) (0.30).", "periodMm": 100, "depthMm": 30, "profile": { "start": [ "0", "0" ], "section": [ { "line": { "to": [ "0.25 * period", "depth" ] } }, { "line": { "to": [ "0.5 * period", "depth" ] } }, { "line": { "to": [ "0.75 * period", "0" ] } }, { "line": { "to": [ "period", "0" ] } } ] } } ,"micro-bevel-l":{ "schema": 1, "id": "micro-bevel-l", "name": "Micro bevel L", "group": "wood", "source": "A micro bevel on each edge of a 100 mm board: a 45 degree chamfer of 2 mm, the L of a four step range (0.5, 1, 1.5, 2 mm). architextures.org/create, the material panel's Surface Profile list, opened 2026-10-20: the name and the depth-to-period proportion read off its thumbnail (one period drawn 52 px wide, so the proportion is read to about 1/52) (its four steps all read under 3 mm, below what a 52 px thumbnail separates).", "periodMm": 100, "depthMm": 2, "profile": { "start": [ "0", "0" ], "section": [ { "line": { "to": [ "depth", "depth" ] } }, { "line": { "to": [ "period - depth", "depth" ] } }, { "line": { "to": [ "period", "0" ] } } ] } } ,"micro-bevel-m":{ "schema": 1, "id": "micro-bevel-m", "name": "Micro bevel M", "group": "wood", "source": "A micro bevel on each edge of a 100 mm board: a 45 degree chamfer of 1.5 mm, the M of a four step range (0.5, 1, 1.5, 2 mm). architextures.org/create, the material panel's Surface Profile list, opened 2026-10-20: the name and the depth-to-period proportion read off its thumbnail (one period drawn 52 px wide, so the proportion is read to about 1/52) (its four steps all read under 3 mm, below what a 52 px thumbnail separates).", "periodMm": 100, "depthMm": 1.5, "profile": { "start": [ "0", "0" ], "section": [ { "line": { "to": [ "depth", "depth" ] } }, { "line": { "to": [ "period - depth", "depth" ] } }, { "line": { "to": [ "period", "0" ] } } ] } } ,"micro-bevel-s":{ "schema": 1, "id": "micro-bevel-s", "name": "Micro bevel S", "group": "wood", "source": "A micro bevel on each edge of a 100 mm board: a 45 degree chamfer of 1 mm, the S of a four step range (0.5, 1, 1.5, 2 mm). architextures.org/create, the material panel's Surface Profile list, opened 2026-10-20: the name and the depth-to-period proportion read off its thumbnail (one period drawn 52 px wide, so the proportion is read to about 1/52) (its four steps all read under 3 mm, below what a 52 px thumbnail separates).", "periodMm": 100, "depthMm": 1, "profile": { "start": [ "0", "0" ], "section": [ { "line": { "to": [ "depth", "depth" ] } }, { "line": { "to": [ "period - depth", "depth" ] } }, { "line": { "to": [ "period", "0" ] } } ] } } ,"micro-bevel-xs":{ "schema": 1, "id": "micro-bevel-xs", "name": "Micro bevel XS", "group": "wood", "source": "A micro bevel on each edge of a 100 mm board: a 45 degree chamfer of 0.5 mm, the XS of a four step range (0.5, 1, 1.5, 2 mm). architextures.org/create, the material panel's Surface Profile list, opened 2026-10-20: the name and the depth-to-period proportion read off its thumbnail (one period drawn 52 px wide, so the proportion is read to about 1/52) (its four steps all read under 3 mm, below what a 52 px thumbnail separates).", "periodMm": 100, "depthMm": 0.5, "profile": { "start": [ "0", "0" ], "section": [ { "line": { "to": [ "depth", "depth" ] } }, { "line": { "to": [ "period - depth", "depth" ] } }, { "line": { "to": [ "period", "0" ] } } ] } } ,"mission-s":{ "schema": 1, "id": "mission-s", "name": "Mission S", "group": "ceramic", "source": "One symmetric S per cover width: the round corrugation of `corrugated-sheet` (two tangent circular arcs), the roll and the pan equally wide. 300 mm cover width, the cover of the library's `roman-tile` and `pantile` (Wienerberger Double Roman and double pantile, recorded in pattern/src/library_tests/profile.rs). architextures.org/create, the material panel's Surface Profile list, opened 2026-10-20: the name and the depth-to-period proportion read off its thumbnail (one period drawn 52 px wide, so the proportion is read to about 1/52) (0.22).", "periodMm": 300, "depthMm": 66, "profile": { "start": [ "0", "0" ], "section": [ { "arc": { "center": [ "0", "(period * period / 4 + depth * depth) / (4 * depth)" ], "from": [ "0", "0" ], "to": [ "0.25 * period", "0.5 * depth" ], "clockwise": false } }, { "arc": { "center": [ "0.5 * period", "depth - (period * period / 4 + depth * depth) / (4 * depth)" ], "from": [ "0.25 * period", "0.5 * depth" ], "to": [ "0.75 * period", "0.5 * depth" ], "clockwise": true } }, { "arc": { "center": [ "period", "(period * period / 4 + depth * depth) / (4 * depth)" ], "from": [ "0.75 * period", "0.5 * depth" ], "to": [ "period", "0" ], "clockwise": false } } ] } } ,"planed-all-round-117":{ "schema": 1, "id": "planed-all-round-117", "name": "Planed all round 117", "group": "wood", "source": "A square edged planed board with the arris eased: a 45 degree chamfer of 2 mm on each edge. The number in the name is the period, mm: the cover one board takes on the wall. 92 and 142 are sourced ThermoWood cladding widths (Beesley & Fildes 20 x 92 mm ThermoWood TIGA rainscreen; Lunawood Luna Bevel HF 26 x 142, 121 mm coverage; both opened 2026-10-20), 66 and 117 are the steps of the same series as Architextures lists them. architextures.org/create, the material panel's Surface Profile list, opened 2026-10-20: the name and the depth-to-period proportion read off its thumbnail (one period drawn 52 px wide, so the proportion is read to about 1/52) (depth read at 2.6, 1.8, 2.3 and 2.8 mm over the four covers).", "periodMm": 117, "depthMm": 2, "profile": { "start": [ "0", "0" ], "section": [ { "line": { "to": [ "depth", "depth" ] } }, { "line": { "to": [ "period - depth", "depth" ] } }, { "line": { "to": [ "period", "0" ] } } ] } } ,"planed-all-round-142":{ "schema": 1, "id": "planed-all-round-142", "name": "Planed all round 142", "group": "wood", "source": "A square edged planed board with the arris eased: a 45 degree chamfer of 2 mm on each edge. The number in the name is the period, mm: the cover one board takes on the wall. 92 and 142 are sourced ThermoWood cladding widths (Beesley & Fildes 20 x 92 mm ThermoWood TIGA rainscreen; Lunawood Luna Bevel HF 26 x 142, 121 mm coverage; both opened 2026-10-20), 66 and 117 are the steps of the same series as Architextures lists them. architextures.org/create, the material panel's Surface Profile list, opened 2026-10-20: the name and the depth-to-period proportion read off its thumbnail (one period drawn 52 px wide, so the proportion is read to about 1/52) (depth read at 2.6, 1.8, 2.3 and 2.8 mm over the four covers).", "periodMm": 142, "depthMm": 2, "profile": { "start": [ "0", "0" ], "section": [ { "line": { "to": [ "depth", "depth" ] } }, { "line": { "to": [ "period - depth", "depth" ] } }, { "line": { "to": [ "period", "0" ] } } ] } } ,"planed-all-round-66":{ "schema": 1, "id": "planed-all-round-66", "name": "Planed all round 66", "group": "wood", "source": "A square edged planed board with the arris eased: a 45 degree chamfer of 2 mm on each edge. The number in the name is the period, mm: the cover one board takes on the wall. 92 and 142 are sourced ThermoWood cladding widths (Beesley & Fildes 20 x 92 mm ThermoWood TIGA rainscreen; Lunawood Luna Bevel HF 26 x 142, 121 mm coverage; both opened 2026-10-20), 66 and 117 are the steps of the same series as Architextures lists them. architextures.org/create, the material panel's Surface Profile list, opened 2026-10-20: the name and the depth-to-period proportion read off its thumbnail (one period drawn 52 px wide, so the proportion is read to about 1/52) (depth read at 2.6, 1.8, 2.3 and 2.8 mm over the four covers).", "periodMm": 66, "depthMm": 2, "profile": { "start": [ "0", "0" ], "section": [ { "line": { "to": [ "depth", "depth" ] } }, { "line": { "to": [ "period - depth", "depth" ] } }, { "line": { "to": [ "period", "0" ] } } ] } } ,"planed-all-round-92":{ "schema": 1, "id": "planed-all-round-92", "name": "Planed all round 92", "group": "wood", "source": "A square edged planed board with the arris eased: a 45 degree chamfer of 2 mm on each edge. The number in the name is the period, mm: the cover one board takes on the wall. 92 and 142 are sourced ThermoWood cladding widths (Beesley & Fildes 20 x 92 mm ThermoWood TIGA rainscreen; Lunawood Luna Bevel HF 26 x 142, 121 mm coverage; both opened 2026-10-20), 66 and 117 are the steps of the same series as Architextures lists them. architextures.org/create, the material panel's Surface Profile list, opened 2026-10-20: the name and the depth-to-period proportion read off its thumbnail (one period drawn 52 px wide, so the proportion is read to about 1/52) (depth read at 2.6, 1.8, 2.3 and 2.8 mm over the four covers).", "periodMm": 92, "depthMm": 2, "profile": { "start": [ "0", "0" ], "section": [ { "line": { "to": [ "depth", "depth" ] } }, { "line": { "to": [ "period - depth", "depth" ] } }, { "line": { "to": [ "period", "0" ] } } ] } } ,"rainscreen-117":{ "schema": 1, "id": "rainscreen-117", "name": "Rainscreen 117", "group": "wood", "source": "An open jointed rainscreen board: the face is flat and splays 13 mm down into the open joint at 45 degrees at one edge, which is the shadow the gap casts. The number in the name is the period, mm: the cover one board takes on the wall. 92 and 142 are sourced ThermoWood cladding widths (Beesley & Fildes 20 x 92 mm ThermoWood TIGA rainscreen; Lunawood Luna Bevel HF 26 x 142, 121 mm coverage; both opened 2026-10-20), 66 and 117 are the steps of the same series as Architextures lists them. architextures.org/create, the material panel's Surface Profile list, opened 2026-10-20: the name and the depth-to-period proportion read off its thumbnail (one period drawn 52 px wide, so the proportion is read to about 1/52) (depth read at 13.2, 14.4, 11.7 and 13.9 mm over the four covers).", "periodMm": 117, "depthMm": 13, "profile": { "start": [ "0", "0" ], "section": [ { "line": { "to": [ "depth", "depth" ] } }, { "line": { "to": [ "period", "depth" ] } } ] } } ,"rainscreen-142":{ "schema": 1, "id": "rainscreen-142", "name": "Rainscreen 142", "group": "wood", "source": "An open jointed rainscreen board: the face is flat and splays 13 mm down into the open joint at 45 degrees at one edge, which is the shadow the gap casts. The number in the name is the period, mm: the cover one board takes on the wall. 92 and 142 are sourced ThermoWood cladding widths (Beesley & Fildes 20 x 92 mm ThermoWood TIGA rainscreen; Lunawood Luna Bevel HF 26 x 142, 121 mm coverage; both opened 2026-10-20), 66 and 117 are the steps of the same series as Architextures lists them. architextures.org/create, the material panel's Surface Profile list, opened 2026-10-20: the name and the depth-to-period proportion read off its thumbnail (one period drawn 52 px wide, so the proportion is read to about 1/52) (depth read at 13.2, 14.4, 11.7 and 13.9 mm over the four covers).", "periodMm": 142, "depthMm": 13, "profile": { "start": [ "0", "0" ], "section": [ { "line": { "to": [ "depth", "depth" ] } }, { "line": { "to": [ "period", "depth" ] } } ] } } ,"rainscreen-66":{ "schema": 1, "id": "rainscreen-66", "name": "Rainscreen 66", "group": "wood", "source": "An open jointed rainscreen board: the face is flat and splays 13 mm down into the open joint at 45 degrees at one edge, which is the shadow the gap casts. The number in the name is the period, mm: the cover one board takes on the wall. 92 and 142 are sourced ThermoWood cladding widths (Beesley & Fildes 20 x 92 mm ThermoWood TIGA rainscreen; Lunawood Luna Bevel HF 26 x 142, 121 mm coverage; both opened 2026-10-20), 66 and 117 are the steps of the same series as Architextures lists them. architextures.org/create, the material panel's Surface Profile list, opened 2026-10-20: the name and the depth-to-period proportion read off its thumbnail (one period drawn 52 px wide, so the proportion is read to about 1/52) (depth read at 13.2, 14.4, 11.7 and 13.9 mm over the four covers).", "periodMm": 66, "depthMm": 13, "profile": { "start": [ "0", "0" ], "section": [ { "line": { "to": [ "depth", "depth" ] } }, { "line": { "to": [ "period", "depth" ] } } ] } } ,"rainscreen-92":{ "schema": 1, "id": "rainscreen-92", "name": "Rainscreen 92", "group": "wood", "source": "An open jointed rainscreen board: the face is flat and splays 13 mm down into the open joint at 45 degrees at one edge, which is the shadow the gap casts. The number in the name is the period, mm: the cover one board takes on the wall. 92 and 142 are sourced ThermoWood cladding widths (Beesley & Fildes 20 x 92 mm ThermoWood TIGA rainscreen; Lunawood Luna Bevel HF 26 x 142, 121 mm coverage; both opened 2026-10-20), 66 and 117 are the steps of the same series as Architextures lists them. architextures.org/create, the material panel's Surface Profile list, opened 2026-10-20: the name and the depth-to-period proportion read off its thumbnail (one period drawn 52 px wide, so the proportion is read to about 1/52) (depth read at 13.2, 14.4, 11.7 and 13.9 mm over the four covers).", "periodMm": 92, "depthMm": 13, "profile": { "start": [ "0", "0" ], "section": [ { "line": { "to": [ "depth", "depth" ] } }, { "line": { "to": [ "period", "depth" ] } } ] } } ,"ribbed":{ "schema": 1, "id": "ribbed", "name": "Ribbed", "group": "metal", "source": "One circular dish per period: the arc through the two period lines and the trough at mid period, radius (period^2/4 + depth^2) / (2 depth). architextures.org/create, the material panel's Surface Profile list, opened 2026-10-20: the name and the depth-to-period proportion read off its thumbnail (one period drawn 52 px wide, so the proportion is read to about 1/52) (0.43).", "periodMm": 100, "depthMm": 43, "profile": { "start": [ "0", "depth" ], "section": [ { "arc": { "center": [ "0.5 * period", "(period * period / 4 + depth * depth) / (2 * depth)" ], "from": [ "0", "depth" ], "to": [ "period", "depth" ], "clockwise": false } } ] } } ,"roman-2":{ "schema": 1, "id": "roman-2", "name": "Roman 2", "group": "ceramic", "source": "A single semicircular roll of 0.4 of the cover width standing on a flat pan, so the depth is a fifth of the cover. 300 mm cover width, the cover of the library's `roman-tile` and `pantile` (Wienerberger Double Roman and double pantile, recorded in pattern/src/library_tests/profile.rs). architextures.org/create, the material panel's Surface Profile list, opened 2026-10-20: the name and the depth-to-period proportion read off its thumbnail (one period drawn 52 px wide, so the proportion is read to about 1/52) (0.20).", "periodMm": 300, "depthMm": 60, "profile": { "start": [ "0", "0" ], "section": [ { "line": { "to": [ "0.3 * period", "0" ] } }, { "arc": { "center": [ "0.5 * period", "0" ], "from": [ "0.3 * period", "0" ], "to": [ "0.7 * period", "0" ], "clockwise": true } }, { "line": { "to": [ "period", "0" ] } } ] } } ,"sawtooth":{ "schema": 1, "id": "sawtooth", "name": "Sawtooth", "group": "metal", "source": "A 45 degree saw tooth: the top falls one period over one period and steps back up at the period line. architextures.org/create, the material panel's Surface Profile list, opened 2026-10-20: the name and the depth-to-period proportion read off its thumbnail (one period drawn 52 px wide, so the proportion is read to about 1/52) (proportion 0.96, i.e. 45 degrees within the reading).", "periodMm": 100, "depthMm": 100, "profile": { "start": [ "0", "0" ], "section": [ { "line": { "to": [ "0", "depth" ] } }, { "line": { "to": [ "period", "0" ] } } ] } } ,"shadow-gap-117":{ "schema": 1, "id": "shadow-gap-117", "name": "Shadow gap 117", "group": "wood", "source": "A shadow gap (secret fixed) board: a square recess 10 mm wide and 10 mm deep at one edge, then the flat face. The number in the name is the period, mm: the cover one board takes on the wall. 92 and 142 are sourced ThermoWood cladding widths (Beesley & Fildes 20 x 92 mm ThermoWood TIGA rainscreen; Lunawood Luna Bevel HF 26 x 142, 121 mm coverage; both opened 2026-10-20), 66 and 117 are the steps of the same series as Architextures lists them. architextures.org/create, the material panel's Surface Profile list, opened 2026-10-20: the name and the depth-to-period proportion read off its thumbnail (one period drawn 52 px wide, so the proportion is read to about 1/52) (depth read at 10.6, 9.2, 9.4 and 8.5 mm over the four covers).", "periodMm": 117, "depthMm": 10, "profile": { "start": [ "0", "0" ], "section": [ { "line": { "to": [ "depth", "0" ] } }, { "line": { "to": [ "depth", "depth" ] } }, { "line": { "to": [ "period", "depth" ] } } ] } } ,"shadow-gap-142":{ "schema": 1, "id": "shadow-gap-142", "name": "Shadow gap 142", "group": "wood", "source": "A shadow gap (secret fixed) board: a square recess 10 mm wide and 10 mm deep at one edge, then the flat face. The number in the name is the period, mm: the cover one board takes on the wall. 92 and 142 are sourced ThermoWood cladding widths (Beesley & Fildes 20 x 92 mm ThermoWood TIGA rainscreen; Lunawood Luna Bevel HF 26 x 142, 121 mm coverage; both opened 2026-10-20), 66 and 117 are the steps of the same series as Architextures lists them. architextures.org/create, the material panel's Surface Profile list, opened 2026-10-20: the name and the depth-to-period proportion read off its thumbnail (one period drawn 52 px wide, so the proportion is read to about 1/52) (depth read at 10.6, 9.2, 9.4 and 8.5 mm over the four covers).", "periodMm": 142, "depthMm": 10, "profile": { "start": [ "0", "0" ], "section": [ { "line": { "to": [ "depth", "0" ] } }, { "line": { "to": [ "depth", "depth" ] } }, { "line": { "to": [ "period", "depth" ] } } ] } } ,"shadow-gap-66":{ "schema": 1, "id": "shadow-gap-66", "name": "Shadow gap 66", "group": "wood", "source": "A shadow gap (secret fixed) board: a square recess 10 mm wide and 10 mm deep at one edge, then the flat face. The number in the name is the period, mm: the cover one board takes on the wall. 92 and 142 are sourced ThermoWood cladding widths (Beesley & Fildes 20 x 92 mm ThermoWood TIGA rainscreen; Lunawood Luna Bevel HF 26 x 142, 121 mm coverage; both opened 2026-10-20), 66 and 117 are the steps of the same series as Architextures lists them. architextures.org/create, the material panel's Surface Profile list, opened 2026-10-20: the name and the depth-to-period proportion read off its thumbnail (one period drawn 52 px wide, so the proportion is read to about 1/52) (depth read at 10.6, 9.2, 9.4 and 8.5 mm over the four covers).", "periodMm": 66, "depthMm": 10, "profile": { "start": [ "0", "0" ], "section": [ { "line": { "to": [ "depth", "0" ] } }, { "line": { "to": [ "depth", "depth" ] } }, { "line": { "to": [ "period", "depth" ] } } ] } } ,"shadow-gap-92":{ "schema": 1, "id": "shadow-gap-92", "name": "Shadow gap 92", "group": "wood", "source": "A shadow gap (secret fixed) board: a square recess 10 mm wide and 10 mm deep at one edge, then the flat face. The number in the name is the period, mm: the cover one board takes on the wall. 92 and 142 are sourced ThermoWood cladding widths (Beesley & Fildes 20 x 92 mm ThermoWood TIGA rainscreen; Lunawood Luna Bevel HF 26 x 142, 121 mm coverage; both opened 2026-10-20), 66 and 117 are the steps of the same series as Architextures lists them. architextures.org/create, the material panel's Surface Profile list, opened 2026-10-20: the name and the depth-to-period proportion read off its thumbnail (one period drawn 52 px wide, so the proportion is read to about 1/52) (depth read at 10.6, 9.2, 9.4 and 8.5 mm over the four covers).", "periodMm": 92, "depthMm": 10, "profile": { "start": [ "0", "0" ], "section": [ { "line": { "to": [ "depth", "0" ] } }, { "line": { "to": [ "depth", "depth" ] } }, { "line": { "to": [ "period", "depth" ] } } ] } } ,"slope":{ "schema": 1, "id": "slope", "name": "Slope", "group": "metal", "source": "A ramp climbing over 0.6 of the period, a short crown, a steeper fall and a flat pan. architextures.org/create, the material panel's Surface Profile list, opened 2026-10-20: the name and the depth-to-period proportion read off its thumbnail (one period drawn 52 px wide, so the proportion is read to about 1/52) (0.31).", "periodMm": 100, "depthMm": 31, "profile": { "start": [ "0", "0" ], "section": [ { "line": { "to": [ "0.6 * period", "depth" ] } }, { "line": { "to": [ "0.74 * period", "depth" ] } }, { "line": { "to": [ "0.9 * period", "0" ] } }, { "line": { "to": [ "period", "0" ] } } ] } } ,"spanish-s":{ "schema": 1, "id": "spanish-s", "name": "Spanish S", "group": "ceramic", "source": "An S whose roll takes 0.4 of the cover width and whose pan takes the rest: the Spanish tile's roll is the narrower and deeper one. 300 mm cover width, the cover of the library's `roman-tile` and `pantile` (Wienerberger Double Roman and double pantile, recorded in pattern/src/library_tests/profile.rs). architextures.org/create, the material panel's Surface Profile list, opened 2026-10-20: the name and the depth-to-period proportion read off its thumbnail (one period drawn 52 px wide, so the proportion is read to about 1/52) (0.24).", "periodMm": 300, "depthMm": 72, "profile": { "start": [ "0", "0" ], "section": [ { "bezier": { "c1": [ "0.1 * period", "0" ], "c2": [ "0.1 * period", "depth" ], "to": [ "0.2 * period", "depth" ] } }, { "bezier": { "c1": [ "0.3 * period", "depth" ], "c2": [ "0.32 * period", "0" ], "to": [ "0.4 * period", "0" ] } }, { "line": { "to": [ "period", "0" ] } } ] } } ,"square":{ "schema": 1, "id": "square", "name": "Square", "group": "metal", "source": "A square wave: half the period at the crest, a vertical step, half at the pan. architextures.org/create, the material panel's Surface Profile list, opened 2026-10-20: the name and the depth-to-period proportion read off its thumbnail (one period drawn 52 px wide, so the proportion is read to about 1/52) (0.50).", "periodMm": 100, "depthMm": 50, "profile": { "start": [ "0", "depth" ], "section": [ { "line": { "to": [ "0.5 * period", "depth" ] } }, { "line": { "to": [ "0.5 * period", "0" ] } }, { "line": { "to": [ "period", "0" ] } } ] } } ,"tongue-and-groove-117":{ "schema": 1, "id": "tongue-and-groove-117", "name": "Tongue & groove 117", "group": "wood", "source": "A V jointed tongue and groove board: a 45 degree chamfer of 5 mm on each edge, so two boards leave a 10 mm wide, 5 mm deep V. The number in the name is the period, mm: the cover one board takes on the wall. 92 and 142 are sourced ThermoWood cladding widths (Beesley & Fildes 20 x 92 mm ThermoWood TIGA rainscreen; Lunawood Luna Bevel HF 26 x 142, 121 mm coverage; both opened 2026-10-20), 66 and 117 are the steps of the same series as Architextures lists them. architextures.org/create, the material panel's Surface Profile list, opened 2026-10-20: the name and the depth-to-period proportion read off its thumbnail (one period drawn 52 px wide, so the proportion is read to about 1/52) (depth read at 5.2, 5.4, 4.6 and 5.5 mm over the four covers).", "periodMm": 117, "depthMm": 5, "profile": { "start": [ "0", "0" ], "section": [ { "line": { "to": [ "depth", "depth" ] } }, { "line": { "to": [ "period - depth", "depth" ] } }, { "line": { "to": [ "period", "0" ] } } ] } } ,"tongue-and-groove-142":{ "schema": 1, "id": "tongue-and-groove-142", "name": "Tongue & groove 142", "group": "wood", "source": "A V jointed tongue and groove board: a 45 degree chamfer of 5 mm on each edge, so two boards leave a 10 mm wide, 5 mm deep V. The number in the name is the period, mm: the cover one board takes on the wall. 92 and 142 are sourced ThermoWood cladding widths (Beesley & Fildes 20 x 92 mm ThermoWood TIGA rainscreen; Lunawood Luna Bevel HF 26 x 142, 121 mm coverage; both opened 2026-10-20), 66 and 117 are the steps of the same series as Architextures lists them. architextures.org/create, the material panel's Surface Profile list, opened 2026-10-20: the name and the depth-to-period proportion read off its thumbnail (one period drawn 52 px wide, so the proportion is read to about 1/52) (depth read at 5.2, 5.4, 4.6 and 5.5 mm over the four covers).", "periodMm": 142, "depthMm": 5, "profile": { "start": [ "0", "0" ], "section": [ { "line": { "to": [ "depth", "depth" ] } }, { "line": { "to": [ "period - depth", "depth" ] } }, { "line": { "to": [ "period", "0" ] } } ] } } ,"tongue-and-groove-66":{ "schema": 1, "id": "tongue-and-groove-66", "name": "Tongue & groove 66", "group": "wood", "source": "A V jointed tongue and groove board: a 45 degree chamfer of 5 mm on each edge, so two boards leave a 10 mm wide, 5 mm deep V. The number in the name is the period, mm: the cover one board takes on the wall. 92 and 142 are sourced ThermoWood cladding widths (Beesley & Fildes 20 x 92 mm ThermoWood TIGA rainscreen; Lunawood Luna Bevel HF 26 x 142, 121 mm coverage; both opened 2026-10-20), 66 and 117 are the steps of the same series as Architextures lists them. architextures.org/create, the material panel's Surface Profile list, opened 2026-10-20: the name and the depth-to-period proportion read off its thumbnail (one period drawn 52 px wide, so the proportion is read to about 1/52) (depth read at 5.2, 5.4, 4.6 and 5.5 mm over the four covers).", "periodMm": 66, "depthMm": 5, "profile": { "start": [ "0", "0" ], "section": [ { "line": { "to": [ "depth", "depth" ] } }, { "line": { "to": [ "period - depth", "depth" ] } }, { "line": { "to": [ "period", "0" ] } } ] } } ,"tongue-and-groove-92":{ "schema": 1, "id": "tongue-and-groove-92", "name": "Tongue & groove 92", "group": "wood", "source": "A V jointed tongue and groove board: a 45 degree chamfer of 5 mm on each edge, so two boards leave a 10 mm wide, 5 mm deep V. The number in the name is the period, mm: the cover one board takes on the wall. 92 and 142 are sourced ThermoWood cladding widths (Beesley & Fildes 20 x 92 mm ThermoWood TIGA rainscreen; Lunawood Luna Bevel HF 26 x 142, 121 mm coverage; both opened 2026-10-20), 66 and 117 are the steps of the same series as Architextures lists them. architextures.org/create, the material panel's Surface Profile list, opened 2026-10-20: the name and the depth-to-period proportion read off its thumbnail (one period drawn 52 px wide, so the proportion is read to about 1/52) (depth read at 5.2, 5.4, 4.6 and 5.5 mm over the four covers).", "periodMm": 92, "depthMm": 5, "profile": { "start": [ "0", "0" ], "section": [ { "line": { "to": [ "depth", "depth" ] } }, { "line": { "to": [ "period - depth", "depth" ] } }, { "line": { "to": [ "period", "0" ] } } ] } } ,"triangle-rib":{ "schema": 1, "id": "triangle-rib", "name": "Triangle", "group": "metal", "source": "An isoceles tooth: the crest at mid period and flanks at 45 degrees (depth = half the period). architextures.org/create, the material panel's Surface Profile list, opened 2026-10-20: the name and the depth-to-period proportion read off its thumbnail (one period drawn 52 px wide, so the proportion is read to about 1/52) (0.49).", "periodMm": 100, "depthMm": 50, "profile": { "start": [ "0", "0" ], "section": [ { "line": { "to": [ "0.5 * period", "depth" ] } }, { "line": { "to": [ "period", "0" ] } } ] } } ,"wave":{ "schema": 1, "id": "wave", "name": "Wave", "group": "metal", "source": "The round corrugation of `corrugated-sheet` (two tangent circular arcs per period) run deep: depth = half the period. architextures.org/create, the material panel's Surface Profile list, opened 2026-10-20: the name and the depth-to-period proportion read off its thumbnail (one period drawn 52 px wide, so the proportion is read to about 1/52) (0.49).", "periodMm": 100, "depthMm": 50, "profile": { "start": [ "0", "0" ], "section": [ { "arc": { "center": [ "0", "(period * period / 4 + depth * depth) / (4 * depth)" ], "from": [ "0", "0" ], "to": [ "0.25 * period", "0.5 * depth" ], "clockwise": false } }, { "arc": { "center": [ "0.5 * period", "depth - (period * period / 4 + depth * depth) / (4 * depth)" ], "from": [ "0.25 * period", "0.5 * depth" ], "to": [ "0.75 * period", "0.5 * depth" ], "clockwise": true } }, { "arc": { "center": [ "period", "(period * period / 4 + depth * depth) / (4 * depth)" ], "from": [ "0.75 * period", "0.5 * depth" ], "to": [ "period", "0" ], "clockwise": false } } ] } } },"presets":{"01-oak-herringbone":{ "id": "oak-herringbone", "name": "Oak herringbone", "category": "Wood floors", "pattern": { "id": "herringbone", "parameters": { "length": 600, "width": 120 } }, "layout": { "angle": 45, "grout": 3.0, "thickness": 14, "bevel": 0.8, "groutRecess": 2.5 }, "groutColor": "#d8d2c8", "materials": [ { "texture": "wood_oak_grain", "variants": 1, "tone": 0, "adjust": { "saturation": 0.25, "brightness": 0.08 } } ] } }}