The 43,252,003,274,489,856,000 number disregards the orientation of center tiles. You'd have to multiply it by 4^4 or something to do the faces. (I can't remem

The 43,252,003,274,489,856,000 number disregards the orientation of center tiles. You'd have to multiply it by 4^4 or something to do the faces. (I can't remember if there is one face or two that are determined by the others, but they're not independent.) The number is derived here (with computer assistance), by considering the permutations of the non-center tiles: https://www.gap-system.org/Doc/Examples/rubik.html https://www.gap-system.org/Doc/Examples/rubik.html