2026-08-04

2D Rubiks Cube

A different way to visualise the underlying group theory of a Rubik's Cube.

Reprojection

Inspired by this video, I created this interactive version. It's a 2D projection of a 3D Rubiks cube, showing the group permutations.

Clicking the square center facelets selects the corresponding face of the cube. Arrow keys (or the rotation buttons in the bottom corners) rotate that face.

The "Show Cube" button displays the equivalent state for a regular Rubik's Cube.

Decoupled Faces

This got me thinking though; the intuitive way for this graph to function is for the facelets to move only on the loops. There is nothing to visually indicate the coupling that a real Rubiks cube has.

Here is a variant of the puzzle that decouples faces from one another. You can select the center facelets like in the previous one, but in this version, you can also select the loops:

This actually captures the way many people think of a 3x3 cube when they first look at it. They usually wont make the connection that the edge/corner pieces are orientable.

In this version, there's no difference between the different corner/edge dots. There are now multiple solutions, as it doesn't matter which corner a piece is in, as long as it's on the right face.

In my opinion, it's also more satisfying to watch it auto-solve.

I'm not sure how to make this kind of cube manufacturable, but I have a feeling that it's possible.