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The Rubik's Cube group (,) represents the structure of the Rubik's Cube mechanical puzzle. Each element of the set corresponds to a cube move, which is the effect of any sequence of rotations of the cube's faces. With this representation, not only can any cube move be represented, but any position of the cube as well, by detailing the cube ...
In five-dimensional geometry, a 5-cube is a name for a five-dimensional hypercube with 32 vertices, 80 edges, 80 square faces, 40 cubic cells, and 10 tesseract 4-faces. It is represented by Schläfli symbol {4,3,3,3} or {4,3 3 }, constructed as 3 tesseracts, {4,3,3}, around each cubic ridge .
Mathematically, edge-matching puzzles are two-dimensional. A 3D edge-matching puzzle is such a puzzle that is not flat in Euclidean space, so involves tiling a three-dimensional area such as the surface of a regular polyhedron. As before, polygonal pieces have distinguished edges to require that the edges of adjacent pieces match.
In geometry, an 8-cube is an eight-dimensional hypercube. It has 256 vertices, 1024 edges, 1792 square faces, 1792 cubic cells, 1120 tesseract 4-faces, 448 5-cube 5-faces, 112 6-cube 6-faces, and 16 7-cube 7-faces. It is represented by Schläfli symbol {4,3 6}, being composed of 3 7-cubes around each 6-face.
In geometry, a tesseract or 4-cube is a four-dimensional hypercube, analogous to a two-dimensional square and a three-dimensional cube. [1] Just as the perimeter of the square consists of four edges and the surface of the cube consists of six square faces , the hypersurface of the tesseract consists of eight cubical cells , meeting at right ...
A three-dimensional edge-matching puzzle is a type of edge-matching puzzle or tiling puzzle involving tiling a three-dimensional area with (typically regular) polygonal pieces whose edges are distinguished with colors or patterns, in such a way that the edges of adjacent pieces match.
A solved Rubik's Revenge cube. The Rubik's Revenge (also known as the 4×4×4 Rubik's Cube) is a 4×4×4 version of the Rubik's Cube.It was released in 1981. Invented by Péter Sebestény, the cube was nearly called the Sebestény Cube until a somewhat last-minute decision changed the puzzle's name to attract fans of the original Rubik's Cube. [1]
3D model of a truncated cube. In geometry, the truncated cube, or truncated hexahedron, is an Archimedean solid. It has 14 regular faces (6 octagonal and 8 triangular), 36 edges, and 24 vertices. If the truncated cube has unit edge length, its dual triakis octahedron has edges of lengths 2 and δ S +1, where δ S is the silver ratio, √ 2 +1.
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