3.11.1
Summary:
This puzzle consists of 8 spherical pieces, just like a 2x2x2 Rubik's Cube.
Each click turns 4 pieces by 90° around a face center of the cube,
while each piece turns around itself by 120°, around the axis between the face center and its own center.
The color scheme A consists of 8 identical pieces, while the color scheme B is of 8 distinct pieces.
| A | B
|
 |
 |
Mathematical properties:
· The permutation group of pieces is S8.
· Any piece can be at any of 8 places, and can
have any of 12 orientations(A4).
So, the total number of possible scrambles is
(8!) ×(12^8) = 17,336,861,982,720.
Solution:
No proof yet, but most scrambles can be reduced to 2x2x2 subgroup within 4 moves(if a series of moves around the same axis is counted as 1).
And then, you can solve as 2x2x2 with only 3,6,9 twists.
This method is inefficient if every 90° twist is counted as one.