Cube the hypercube graph. It is one of 5 Platonic graphs, each a skeleton of its Platonic solid. An extension is the three dimensional "k"-ary Hamming graph, which for "k" = 2 is the cube graph. Graphs of this sort occur in the theory of parallel processing in computers. Miscellaneous cubes Cube In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. The cube is the only regular hexahedron and is one of the five Platonic solids. It has 6 faces, 12 edges, and 8 vertices. The cube
V-Cube 6 the internal shape of the pieces is asymmetrical), nor can an inner edge exchange places with an outer edge. The four edges in each matching quartet are distinguishable, since corresponding edges are mirror images of each other. Any permutation of the edges in each set is possible, including odd permutations, giving 24! arrangements for each set or 24! total, regardless of the position or orientation any other pieces. Assuming the cube does not have a fixed orientation in space, and that the permutations resulting from rotating the cube without twisting it are considered identical, the number of permutations is reduced