Rubik's Cube could be coloured in such a way as to emphasise the corners or edges, rather than the faces as the standard colouring does; but neither of these alternative colourings has ever become popular. The original (3×3×3) Rubik's Cube has eight corners and twelve edges. There are 8! (40,320) ways to arrange the corner cubes. Each corner has three possible orientations, although only seven (of eight) can be oriented independently; the orientation of the eighth (final) corner depends on the preceding seven, giving 3 (2,187) possibilities. There are 12!/2 (239,500,800) ways to arrange the edges, restricted from 12! because edges must
Folded cube graph nearly the same vertex degree but only half the diameter. Efficient distributed algorithms (relative to those for a "hypercube") are known for broadcasting information in a folded cube. Folded cube graph In graph theory, a folded cube graph is an undirected graph formed from a hypercube graph by adding to it a perfect matching that connects "opposite" pairs of hypercube vertices. The folded cube graph of order "k" (containing 2 vertices) may be formed by adding edges between opposite pairs of vertices in a hypercube graph of order "k" − 1. (In a hypercube with 2 vertices, a pair of