Whisker Cube & Simulator

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Designing Twisty Puzzles - Group Theoretical Approach

Photos

Simulator

Video

Details

• Weight: ? g
• Edge length: ~70 mm
• Reachable positions: 3 × 3 × 1344 = 12096
• God’s number (max solution depth): 15

The Extension Cube…

Group Breakdown

The 2³.PSL₃(2) group has 1344 elements. This table shows the frequency of each permutation cycle:

384: dual 7-cycles
224: quadruple 3-cycles
224: single 2-cycle, dual 3-cycles, single 6-cycle
168: single 4-cycle, single 8-cycle
168: triple 2-cycles, single 8-cycle
 84: 6p 2-cycles
 42: dual 2-cycles, dual 4-cycles
 42: dual 4-cycles
  7: quadruple 2-cycles
  1: solved

Solution

Rough solution (edges first):

1. Put WB piece in BOu slot intuitively.
   
   
2. Put GO (or its counterpart GR) in BOd slot by turning the YBO corner.
   • If neither are available on the YBO corner, try X Y (X) Y' X' once or twice until one is in the cycle. Then move it into BOd.
   • If GR was placed, execute (X' Y' X Y)×3 to swap it with GO.
     
     
3. Use Y X to move GO and WB into place.
   
   
4. At this point, 6 pieces are solved and the remaining 8 are either solved, or express a quaternion state.
   • Quaternion i: X Y X Y
   • Quaternion j: Y X Y X (X Y X Y) X' Y' X' Y'
     
     
5. Solve corner parity.
   • Twist both corners clockwise (16 moves): (X Y)x8
   • Twist X counter-clockwise (12 moves): (X Y' X' Y' X Y')×2

Gallery