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
5-cube 5-cube In five-dimensional geometry, a 5-cube is a name for a five-dimensional hypercube with 32 vertices, 80 edges, 80 square faces, 40 cubic cells, and 10 tesseract 4-faces. It is represented by Schläfli symbol {4,3,3,3} or {4,3}, constructed as 3 tesseracts, {4,3,3}, around each cubic ridge. It can be called a penteract, a portmanteau of tesseract (the "4-cube") and "pente" for five (dimensions) in Greek. It can also be called a regular deca-5-tope or decateron, being a 5-dimensional polytope constructed from 10 regular facets. It is a part of an infinite hypercube family. The dual of a 5-cube is the