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
8-cube the column element. The configurations for dual polytopes can be seen by rotating the matrix elements by 180 degrees. formula_1 The diagonal f-vector numbers are derived through the Wythoff construction, dividing the full group order of a subgroup order by removing one mirror at a time. Applying an "alternation" operation, deleting alternating vertices of the octeract, creates another uniform polytope, called a "8-demicube", (part of an infinite family called demihypercubes), which has 16 demihepteractic and 128 8-simplex facets. 8-cube In geometry, an 8-cube is an eight-dimensional hypercube (8-cube). It has 256 vertices, 1024 edges, 1792 square faces, 1792 cubic cells,