if you think of the 4-color cube as four 1-color tetrahedra, the cube core consists of another tetrahedron
4-color cube = Mastermorphix (also known as Master Pyramorphix) in the same way as how 2x2x2 cube = Pyramorphix (clearly, cubes are non-morphing, i.e. they don´t shape-shift, but the mechanism is the same)
on the 6-color and 3-color (same color on opposite faces) cubes, Superflip is a hard position. On the 4-color cube, pure Superflip is a trivial position
the number of combinations and God´s number is known for the 2-color (both cases with having the same color on 3 faces and the other color on remaining 3 faces), 3-color and 6-color cubes, but not for the 4-color cube
If I did the math right, the 4-color cube has a total of [(4^6) * (8!*3^4)]/2 * (12!/(3!)^4) = 2,472,108,097,536,000 or 2.47*10^15 states with respect to fixed centers.
