7.8.7

AB

Summary:

This puzzle consists of 12 cubic pieces. Clicking one of 3 central cubes rotates 6 surrounding cubes around it. Cubes rotate by 90° around the edge with the next cube, and then slide into the next place.
· Type A consists of 12 identical pieces with standard cubic puzzle color scheme.
· Type B consists of 6 non-identical pieces and 3 pairs of 2 identical pieces.

Solved states:

· Type A is considered as solved when all pieces have the same orientation. There are 24 solved states correspondig to 24 orientations of cube.
· Types B is considered as solved when all 2 adjacent faces of 2 adjacent cubes have same colors. That makes appear a black or white hexagon at center with 6 colored hexagons around it. There are 24 visibly different solutions.

Mathematical properties:

· The permutation group of pieces is S12.
· Any piece can be at any of 12 places, and can have any of 24 orientations.
· The sum of parity of cube orientations is always even.
· So, the total number of possible scrambles is (12!)×(2412)÷2=8,746,652,427,213,498,797,260,800.