7.2.7

Summary:

This puzzle consists of 9 diamond-shaped pieces,
with 3 points to click, namely A, B and C. Each click
rotates 7 pieces. 2 Pieces are rotated by 120°
around the center of the puzzle, and 5 pieces
by 60° around one of 3 concave vertices.

After 7 clicks, all pieces are at their
original places but twisted by 180°.

→ [A7] →

Solved states:

There are these 6 solved states.

Mathematical properties:

· The permutations of pieces form a group of order 504. This group is isomorphic to PSL(2,8) and PGL(2,8).

gap> g:=Group((9,1,5,8,7,4,6),(3,4,8,2,1,7,9),(6,7,2,5,4,1,3));
Group([ (1,5,8,7,4,6,9), (1,7,9,3,4,8,2), (1,3,6,7,2,5,4) ])
gap> Size(g);
504
gap> IdSmallGroup(g)=IdSmallGroup(PSL(2,8));
true
gap> IdSmallGroup(g)=IdSmallGroup(PGL(2,8));
true

· Any piece can be at any of 9 places, and can be twisted by (n×180°).
So the total number of possible scrambles is: 504 ×(2^9) = 258,048.

Solution:

This puzzle can be solved in two steps and within 11 moves.
1.Permutate pieces to one of 6 solved states listed above(0~5 moves).
2.Fix the twists preserving the relative positions among all pieces (0~6 moves).

Example:

Step 1
→[C2,A2,B3]→

Step 2
→[C11,A6,B9]→