Video: https://www.youtube.com/watch?v=L3PB-1eoA3I
The Undectrix is a deeper-than-origin, two axis twisty puzzle with some interesting group theoretical properties. It is a doctrinaire puzzle formed by combining an octahedral edge and face cut at a depth of ~107°.
When I started exploring unusual groups in twisty puzzles I wanted to build something that satisfied these constraints:
- Inclusion of at least one ’new’ interesting group
- No gears or mechanical restrictions
- Similar solving difficulty to Trapentrix, the first known biaxe puzzle with exceptional properties
I finally found one that looked unique and feasible enough, thanks to recent discussion around Bram Cohen’s web-based puzzle explorer.
This is a reference guide for designing vinyl decals to fit over a curved surface, using Solidworks or other CAD software. It demonstrates the optimal steps for fine-tuning the shape and offsets of the decal, ending with the surface flattening feature + SVG export available in Onshape. I use this procedure to design stickers for pillowed twisty puzzles.
1. Copy unique surfaces
First, use the Offset Surface tool in Solidworks (or equivalent in your CAD software) to copy each curved surface that gets a sticker. Set the offset to 0 so that the new surface is exactly the same as the original.
This video outlines the entire process of designing the Rocking Cube (PSL₂(13)), including group selection, data refinement & visualization, and mechanical implementation.
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.
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.
Originally published 2025-03-06
Updated 2025-11-05
Video
Solving Guide
Photos
The M12 Cube is an internally geared twisty puzzle that expresses the Mathieu M12 group over its 12 edge pieces.
Video
Solving Guide
Photos
Video: https://www.youtube.com/watch?v=rPHlY3ExgLc
The Triskelion Barrel is another entry in my group theory showcase, this time expressing the PSL₃(3) group over the 13 equilateral triangle pieces. The circles are divided into synchronized sets (marked with red, green, and blue diamond stickers) that turn simultaneously in 180° increments.
I geared the circles together with an external ring gear. Spinning a colored ring causes the corresponding circles to rotate. The mechanism is assembled using a 3D printed kit of axles, bevel gears, and metal pins assembled in layers.
Updated 2025-07-31
The Quaternion Cube is a rather easy-to-solve puzzle that I designed to visually demonstrate the Quaternion Group Q₈.
Introduction
Mora Jai boxes are simple-looking puzzles that can be configured into a huge variety of challenges. The original set of puzzles from Blue Prince mostly have short, simple solutions (2-20 moves), but lengthy and difficult solutions can be constructed by exploring deeper state spaces of the tile grid.
Initially, I wanted to create a list of the most difficult configurations by cataloging the longest solutions, but it turns out that length is not the best predictor of difficulty. Many of the longest solutions rely on repetitive patterns rather than complex logic and novel mechanics.
Ultimately, the list of Challenge puzzles in my simulator was found using a combination of brute-force search, automated filtering, and manual inspection.
Mora Jai Box
A Mora Jai Box is a lock box that involves solving a 3x3 grid of colored tiles. Each color has a unique behavior (see rules). They are originally found in the puzzle/adventure game Blue Prince, but are interesting to analyze on their own.
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.
