Dogic

The Dogic is an icosahedron-shaped puzzle like the Rubik's Cube. The 5 triangles meeting at its tips may be rotated, or 5 entire faces (including the triangles) around the tip may be rotated. It has a total of 80 movable pieces to rearrange, compared to the 20 pieces in the Rubik's Cube.

Read more about Dogic:  History, Description, Solutions, Number of Combinations

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Number of Combinations - 10-color Dogic
... Only even permutations of the centres are possible (2) Centre orientation does not matter (320) Ten of the centres are visually identical to the other ten (210) Some tip pieces are indistinguishable (6!10) The orientation of the puzzle does not matter (60) This leaves positions for the 10-color Dogic. ...