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
5-cube 5-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}, constructed as 3 tesseracts, {4,3,3}, around each cubic ridge. It can be called a penteract, a portmanteau of tesseract (the "4-cube") and "pente" for five (dimensions) in Greek. It can also be called a regular deca-5-tope or decateron, being a 5-dimensional polytope constructed from 10 regular facets. It is a part of an infinite hypercube family. The dual of a 5-cube is the