center pieces adjacent to them make up the supporting frame and these have extensions which hold the rest of the pieces together. This allows smooth and fast rotation and creating arguably the fastest and most durable version of the puzzle at that time. Unlike the original 5×5×5 design, the V-Cube 5 mechanism was designed to allow speedcubing. Most current production 5×5×5 speed cubes have mechanisms based on Verdes' patent. Stability and durability The original Professor's Cube is inherently more delicate than the 3×3×3 Rubik's Cube because of the much greater number of moving parts and pieces. Because of its fragile design, the Rubik's brand Professor's Cube is not suitable for Speedcubing. Applying excessive force to the cube when twisting it may result in broken pieces. Both 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. Permutations 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 corner depends on the other seven, giving 37 (or 2,187) combinations. There are 54 centers. Six of these (the center square of each face) are fixed in position. The rest consist of two sets of 24 centers. Within each set there are four centers of each color. Each set can be arranged in 24! different ways. Assuming that the four centers of each color in each set are indistinguishable, the number of permutations of each set is reduced to 24!/(246) arrangements, all of which are possible. The reducing factor comes about because there are 24 (4!) ways to arrange the four pieces of a given color. This is raised to the sixth power because there are six colors. The total number of permutations of all movable centers is the product of the permutations of the two sets, 24!2/(2412). The 24 outer edges cannot be flipped due to the interior shape of those pieces. Corresponding outer edges are distinguishable, since the pieces are mirror images of each other. Any permutation of the outer edges is possible, including odd permutations, giving 24! arrangements. The 12 central edges can be flipped. Eleven can be flipped and arranged independently, giving 12!/2 × 211 or 12!