| 主权项 |
1. A set of plane-filling, double-sided tiles capable of forming all 17 plane periodic patterns, four three-dimensional Platonic solids, wherein the four three-dimensional Platonic solids are a tetrahedron, a cube, an octahedron and an icosahedron, and, five three-dimensional Archimedean solids, wherein the five three-dimensional Archimedean solids are a truncated tetrahedron, a truncated octahedron, a snub cube, a rhombicuboctahedron and a cuboctahedron, said set comprising:
a. at least six identical tiles of a first type, having a planar right triangular shape, having two faces and three edges consisting of a shorter edge, a longer edge, and a hypotenuse edge, and, having angles of 30°, 60°, and 90° between the edges, and, having a first male coupling element along the shorter edge, a second male coupling element along the longer edge, a third female coupling element along the longer edge, a fourth male coupling element along the hypotenuse edge of the triangle, and, a fifth female coupling element along hypotenuse edge of the triangle, all said coupling elements having a centerline, and, all said coupling elements having a location of the centerlines along the edges, and, b. at least six identical tiles of a second type, having a planar right triangular shape, having two faces and three edges consisting of a shorter edge, a longer edge, and a hypotenuse edge, and, having angles of 30°, 60°, and 90° between the edges, and, having a first female coupling element along the shorter edge, a second female coupling element along the longer edge, a third male coupling element along the longer edge, a fourth female coupling element along the hypotenuse edge of the triangle, and, a fifth male coupling element along the hypotenuse edge of the triangle, all said coupling elements having a centerline, and, all said coupling elements having a location of the centerlines along the edges, and, the locations of the first second, third, fourth, and, fifth coupling elements along the edges being the same as the locations of the first, second, third, fourth and fifth coupling elements of the tiles of the first type along their edges, and, c. at least six identical tiles of a third type said tiles being identical to the tiles of the first type, but further including an asymmetric pattern on each side of each tile, said asymmetric patterns being the same on both sides, and, on all tiles of the third type, and, the patterns having a location and an orientation on the two faces of the tiles, said locations and orientations being the same on all faces and all tiles of the third type, and, d. at least six identical tiles of a fourth type, said tiles being identical to the tiles of the second type, but further including an asymmetric pattern on each side of each tile, said asymmetric patterns being the same on both sides, and, on all tiles of the fourth type, the same as the asymmetric patterns on the tiles of the third type, and, the patterns having a location and an orientation on the faces of the tiles, said locations and orientations being the same on all faces and all tiles of the fourth type, and, said locations and orientations being the same as the locations and orientations of the asymmetric patterns on the tiles of the third type, and, e. the size and location of the coupling elements on the tiles of the first, second, third and fourth types provide for mutual interlocking of the tiles such that the tiles may be interlocked only with long edges adjoined to one another, short edges adjoined to one another and hypotenuses adjoined to one another, and, f. wherein tiles of the first, second, third and fourth type may be selected and joined to form patterns displaying the symmetry of the plane periodic patterns identified in Conway notation as 0, 2222, 22X, XX, ** *X *2222, 2*22, 22*, 333, 632, *333, 3*3 and *632, and, g. at least four identical tiles of a fifth type having a planar right triangular shape with two faces and three edges consisting of a first leg edge, a second leg edge, and a hypotenuse edge, and, having angles of 45°, 45°, and 90° between the edges, and, having a first female coupling element along the first leg edge, and, a second male coupling element along the first leg edge, and, a third female coupling element along the second leg edge, and, a fourth male coupling element along the second leg edge, and, a fifth female coupling element along hypotenuse edge of the triangle, and, a sixth male coupling element along the hypotenuse edge, each of the coupling elements having a centerline and a location along the edge that is defined by the locations of the centerlines, and, h. at least four identical tiles of a sixth type, said tiles being identical to the tiles of the fifth type but further including an asymmetric pattern on each side of each tile, said asymmetric patterns being the same on both sides and on all tiles of the sixth type, and, is the same as the asymmetric patterns on the tiles of the third type, and, the patterns having a location, and, an orientation on the faces of the tiles said locations and orientations being the same on all laces and all tiles of the sixth type, and, i. at least lour identical tiles of a seventh type said tiles being identical to the tiles of the sixth type except that the first third and fifth coupling elements are male coupling elements and the second, fourth and sixth coupling elements are female coupling elements, and, j. the size and location of the coupling elements on the tiles of the fifth, sixth and seventh types provide for mutual interlocking of the tiles such that the tiles may be interlocked only with hypotenuses adjoined to one another and legs joined to one another, and, k. wherein tiles of the fifth, sixth and seventh types may be selected and joined to form patterns displaying the symmetry of the plane periodic patterns identified in Conway notation as 0, 2222, 22X, XX, **, *X, *2222, 2*22, 22*, 442, *442, and, 4*2, and, l. wherein all of the coupling elements are of a ball and socket type, said male coupling elements comprising a ball-shaped structure and said female coupling elements comprising a socket-shaped structure, such that when coupling elements along two mutual edges of the tiles are joined, the two tiles may be rotated relative to one another about an axis of connection between the male and female coupling elements of the mutual edges in a direction perpendicular to the two edges being joined; m. wherein the hypotenuses of all the tiles are the same length; and n. wherein the size and location of the coupling elements on the hypotenuse of the tiles of the first, second, third and fourth types are chosen such that the hypotenuses of the tiles may be adjoined to an edge formed from two short legs of a pair tiles of the first, second, third and fourth type adjoined along their long edges. |
