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3×3×3×3 in Magic Cube 4D

Hypercubing is the hobby of solving twisty puzzles (such as the Rubik’s cube) in higher dimensions. The ways that twisty puzzles move are mathematically well defined, and can be generalized to higher spatial dimensions. These puzzles can then be visualized and simulated using computer software.

The most well known 4D shape is the hypercube (also called the tesseract, 8-cell, octachoron, or 4-cube). It has 8 cubic sides that are called cells. Turning any of the cells involves rotating it like a cube to any of 24 orientations.

The short article Abstracting the Rubik’s Cube introduces a number of the hypercubing puzzles.