Professor's Cube the Eastsheen 5×5×5 and the V-Cube 5 are designed with different mechanisms in an attempt to remedy the fragility of the original design. There are 98 pieces on the exterior of the cube: 8 corners, 36 edges, and 54 centers (48 movable, 6 fixed). Any permutation of the corners is possible, including odd permutations, giving 8! possible arrangements. Seven of the corners can be independently rotated, and the orientation of the eighth depends on the other seven, giving 3 (or 2,187) combinations. There are 54 centers. Six of these (the center square of each face) are fixed in position. The
Soma cube Each solved cube can be rotated such that the "T" piece is on the bottom with its long edge along the front and the "tongue" of the "T" in the bottom center cube (this is the normalized position of the large cube). This can be proven as follows: If you consider all the possible ways that the "T" piece can be placed in the large cube (without regard to any of the other pieces), it will be seen that it will always fill either two corners of the large cube or zero corners. There is no way to orient the