Video: https://www.youtube.com/watch?v=c0AkCcUzcj8
Print it yourself: https://chandler.io/posts/2025/03/print-it-yourself-illegal-slice-cube/
The Illegal Slice Cube continues my exploration of finite group theory in twisty puzzles. It combines two unusual concepts:
Oskar van Deventer’s Illegal Cube
- Fudging permits 90° turns, which normally wouldn’t be allowed on a 3x3 pentagonal prism.
Slice-only puzzles (like Slice Rex Cube)
- Opposite sides turn simultaneously - like a 3x3 Rubik’s cube with middle turns only.
Unlike some of the previous puzzles in this series, this one is pretty difficult to solve.
STL Files: https://quirkycubes.com/public/Illegal Slice Cube STL.zip
Sticker Template: https://quirkycubes.com/public/Illegal Slice Cube Stickers.zip
Hardware required:
- 4x M3 Springs (~10mm uncompressed)
- 4x M3 Washers
- 4x M3 x 8 Screws (socket or button head)
- 4x M3 x 16 Screws (socket or button head)
- 4x M2 x 8 Button Head Screws
- Lubricant
- Super glue (optional)
The Illegal Slice Cube is easy to print and doesn’t require any special hardware.
Bambu P1S print settings:
- 0.16 mm layers
- Support raft
- Half speed
- Auto snug supports at 25-30°
- Manual strong tree supports on core - just the overhangs
- 3 wall loops (for vapor smoothing)
- Polymaker ABS (Bambu brand ABS does not vapor-smooth)
- Bambu Support for ABS
Assembly
The core is made up of multiple parts that must be assembled in a specific order.
The Fano Gem is a twisty puzzle that I designed to showcase the symmetries of the Fano Plane, which is a familiar object in combinatorics, coding theory, and algebra. The Fano Plane is the smallest possible finite projective plane, constructed from 7 points and 7 lines, where each line contains exactly 3 points.
Updated 2025-03-16
STL Files (v2): https://quirkycubes.com/public/QuaternionCube_STL_v2.zip
Sticker Template (SVG, Silhouette Studio): https://quirkycubes.com/public/QuaternionCube_Stickers_v2.zip
Hardware required:
- 5x M3 Springs (~10mm uncompressed)
- 5x M3 Washers (6.9mm dia)
- 5x M3 x 20mm Screws (button or socket)
- 12x M2 x 8 Button Head Screws
- 8x M1.6 x 16 Socket Head Screws
- 7/64" drill bit
I printed my copy out of ABS and vapor-smoothed it to post process it. I don’t see any reason that it wouldn’t work in PLA, but you will need to sand the edge hooks a little to get smooth motion. Here are the settings I use on a Bambu P1S:
DoDot M12
The DoDot M12 is a twisty puzzle that mechanically demonstrates Mathieu group M12. It’s a modification of my original vertex-turning dodecahedron where sets of three turning axes are geared together internally. This gearing was chosen to greatly reduce the number of possible permutations of the ‘dot’ pieces, which behave according to the rules of the 12-element M12 permutation group. The edge pieces of the puzzle behave as 6 disjoint orbits of 5 pieces, which makes them easy to solve. I greyed out the petals to avoid making the puzzle too complicated.
The DoDot puzzle is a variation of the Bauhinia Dodecahedron inspired by David Pitcher’s OctaDot.
The Antler Cube is a modification of the Nón Lá cube that unlocks new moves and a more difficult solve.
Quirky Gem III Puzzle
Quirky Gem II Puzzle
Quirky Gem I Puzzle
