Rocking Cube & Simulator

The Rocking Cube is an internally geared twisty puzzle that expresses the group PSL₂(13) over its 14 edge pieces. This was a difficult puzzle to design, and I published a YouTube video outlining the process.

Designing Twisty Puzzles - Group Theoretical Approach

Photos

Simulator

Video

Details

• Weight: 215 g
• Edge length: ~70 mm
• Reachable positions: 3 × 3 × 1092 = 9828
• God’s number (max solution depth): 16

The Rocking Cube implements one of three possible gearing configurations for expressing PSL₂(13) over a vertex-turning cube. The other two configurations are chiral and produce a slightly different puzzle, with solution depth 15.

PSL₂(13) State Breakdown

The PSL₂(13) group has 1092 elements. This table shows the frequency of each permutation cycle:

468: dual 7-cycles
182: dual 6-cycles
182: quadruple 3-cycles
168: single 13-cycle
 91: 6p 2-cycles
  1: solved

Solution

Rough solution (edges first):

1. Place WO
2. Repeat Y X Y' X until WR is solved (13-cycle)
3. Try X Y X' once or twice — 50/50 chance the edges are solved.
4. If not, switch the parity with Y X (Y' X')×3 Y' X Y X, then repeat step 3.
5. Solve corners:

• X clockwise & Y clockwise: (X Y)×7
• X clockwise: (X' Y X' Y X Y X Y X' Y')×2
• Y counter-clockwise: (X Y X' Y' X' Y' X' Y X' Y)×2

Gallery