7.7.9

ABC

Summary:

This puzzle consists of 6 dodecahedral pieces. Clicking one of 4 triangular centers rotates 3 pieces around it, while each piece spins around an oblique axis through two opposite vertices.
· Type A consists of 6 identical pieces with standard dodecahedral color scheme.
· Type B consists of 3 pairs of 2 identical pieces, each with 6 colors.
· Type C consists of 6 non-identical pieces, each with 3 colors.

Solved states:

· Type A is considered as solved when all pieces have the same orientation. There are 60 solved states correspondig to 60 orientations of dodecahedron.
· Types B and C are considered as solved when all 2 adjacent faces of 2 adjacent pieces have same colors. They have respectively 12 and 6 visibly different solutions.

Mathematical properties:

· The permutation group of pieces is A6.
· Any piece can be at any of 6 places, and can have any of 60 orientations.
· Total number of possible scrambles is (6!)÷2×(606)=16,796,160,000,000.