I felt this was the appropriate place for this question. I'm interested in finding the number of unique positions of a Gigaminx. Edges and corners are simple. But I'm afraid I don't understand the calculations in this thread regarding centres. As I understand it, there are two different kinds of Gigaminx centre pieces, the trapezoidal ones and the rhomb...rhomboid (?) ones.
The Gigaminx only allows even permutations of each type of piece. So, clearly, 3-cycles within one centre are allowable while still being solved. But 2 2-cycles, with them both on the same face or on different faces, are allowable as well. 2 4-cycles, a 5-cycle, etc.
Counting is not my strong suit. How would I go about finding the number of solved positions for a Gigaminx?
A more complicated question, how many unique positions of the Gigaminx are there? That is, how many indistinguishable positions are there? Some positions would be distinguishable Gigaminx "supercube" but not on a regular Gigaminx.
Thanks for the help.