Illegal Slice Cube
Illegal Slice Cube

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.

Print it yourself: Illegal Slice Cube
Print it yourself: Illegal Slice Cube

STL Files: https://quirkycubes.com/public/Illegal Slice Cube STL.zip

Sticker Template: https://quirkycubes.com/public/Illegal Slice Cube Stickers.zip

Hardware required:


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.

Crammed Cube & Simulator
Crammed Cube & Simulator

The Crammed Cube is an internally geared twisty puzzle that expresses the Mathieu M11 group over its 12 edge pieces. The puzzle features a modified Compy Cube mechanism with 6 axes, which are mechanically linked into two sets using universal joints and gears. It is called the ‘Crammed Cube’ because, while the axis system would normally have 11 moving edges, I’ve crammed an extra one into the red/white edge and lifted the corner angle to make space. This edge duplication is necessary to make the group actions fit over cubic geometry.

Fano Gem Puzzle & Simulator
Fano Gem Puzzle & Simulator

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.

From the red face (pictured left), the numbers on the corners of the puzzle match up with the numbers on the plane (with number 7 on the back of the puzzle, out of view).

Hurwitz Quaternion Algebra Simulator
Hurwitz Quaternion Algebra Simulator

A comment on my last YouTube video pointed out that the SL(2,3) group expressed by the Quaternion Cube is isomorphic to the group formed by multiplication of the unit Hurwitz quaternions.

Simulator

‘Order’

There are five different orders of unit Hurwitz quaternions: 1, 2, 3, 4, and 6; On the puzzle, the order represents how many times a sequence must be repeated to return to where you started.

Quaternion Cube
Quaternion Cube

The Quaternion Cube is a rather easy-to-solve puzzle that I designed to visually demonstrate the Quaternion Group Q₈.

The puzzle turns over the top 4 vertices of a cube, with 1:2 gearing connecting the opposing corners. There are linear slides under the edge pieces that prevent the static corners from blocking the overall movement.

The puzzle has 24 possible positions, which express the group SL(2,3). SL(2,3) contains the Quaternion Group (Q₈) as a subgroup, and these Q₈ states are expressed over the 8 edges whenever the corners are solved.

Print it yourself: Quaternion Cube
Print it yourself: Quaternion Cube

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:

Hardware


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:

Geared Mathieu M12 Puzzle
Geared Mathieu M12 Puzzle

DoDot M12

VIDEO

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.

DoDot
DoDot

DoDot Puzzle

The DoDot puzzle is a variation of the Bauhinia Dodecahedron inspired by David Pitcher’s OctaDot.

YouTube Video More information

Antler Cube
Antler Cube

Antler Cube

The Antler Cube is a modification of the Nón Lá cube that unlocks new moves and a more difficult solve.

YouTube Video More information

Mugs
Glaze Material Substitution Calculators
Glaze Material Substitution Calculators

Glaze Material Substitutions

This page provides a set of calculators to help with calculating common material substitutions in glaze recipes.

Warning: These calculators are based on theoretical UMF analysis of the materials, and I have not verified them experimentally. Oxide analysis isn’t the only factor that determines how a material will behave in a glaze.

Each calculator allows for conversions between two material forms. Click “Switch” to toggle the conversion direction. Red cells indicate that a material should be subtracted from the recipe.