Updated 2025-07-31
The Quaternion Cube is a rather easy-to-solve puzzle that I designed to visually demonstrate the Quaternion Group Q₈.
Simulator
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 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.
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).
