This is the number of ways to arrange the pieces on a Megaminx, a dodecahedral puzzle similar in concept to Rubik's Cube. The reasons for the number are similar to those for the 3x3x3 Rubik's cube except for the parity factor, which is the division by 4. On the Megaminx, every turn performs an even permutation on the corners and an even permutation on the edges. Therefore, the total permutation of all the corners is always even, and likewise for the edges.
The decimal expansion of the megaminx puzzle is: 100669616553523347122516032313645505168688116411019768627200000000000