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
Compound of 5-cube and 5-orthoplex cells and edges. Mid-edges of the 5-cube cross mid-cell in the 16-cell, and vice versa. It can be seen as the 5-dimensional analogue of a compound of cube and octahedron. The 42 Cartesian coordinates of the vertices of the compound are. The convex hull of the vertices makes the dual of rectified 5-orthoplex. The intersection of the 5-cube and 5-orthoplex compound is the uniform birectified 5-cube: = ∩ . The compound can be seen in projection as the union of the two polytope graphs. The convex hulll as the dual of the rectified 5-orthoplex will have the same vertices, but