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
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
Gallery
