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
Centered cube number Centered cube number A centered cube number is a centered figurate number that counts the number of points in a three-dimensional pattern formed by a point surrounded by concentric cubical layers of points, with "i" points on the square faces of the "i"-th layer. Equivalently, it is the number of points in a body-centered cubic pattern within a cube that has "n" + 1 points along each of its edges. The first few centered cube numbers are The centered cube number for a pattern with "n" concentric layers around the central point is given by the formula The same number