3.11.1
Summary:
This puzzle is to the Impossiball,
what 3.11.1 is to the Pocket Cube.
Just like the Impossiball, it consists of 20 pieces located at each face of the icosahedron,
but with tetrahedral symmetry instead of a triangular one.
While 5 pieces orbit a vertex of the icosahedron, each of them spins on its own axis
connecting its center and the center of the orbit.
So, after 5 twists, all pieces are at their original places, but twisted by 120°.
Mathematical properties:
· The permutation group of pieces is A20.
· Any piece can be at any of 20 places, and can
have any of 12 orientations(A4).
So, the total number of possible scrambles is
(20!)÷2 ×(12^20) = 4,663,581,192,246,361,212,168,978,867,494,584,320,000.
Solution:
This puzzle can be reduced to the Impossiball,
and then, you can solve only with 3×N (3,6,9,12) moves.