Diameters of Rubik’s Cube graphs

Determine the exact diameters of higher-order Rubik’s Cube graphs and of the 3×3×3 Rubik’s Cube under the STM and ATM metrics.

Background

The paper notes that exact diameters, or God’s numbers, are known only for some puzzle groups and metrics. In particular, the authors identify unresolved diameter questions for higher-order Rubik’s Cubes and for alternative move metrics on the standard 3×3×3 cube.

References

It is widely unknown for most of the puzzles, its determination for the Rubik's cube 3x3x3 for the standard choices of generators required significant efforts and computational resources. It is not known precisely for higher cubes, neither for 3x3x3 Rubik's with \href{https://www.speedsolving.com/wiki/index.php?title=Metric#STM}{STM, ATM} metrics.

— CayleyPy RL: Pathfinding and Reinforcement Learning on Cayley Graphs  (2502.18663 - Chervov et al., 25 Feb 2025) in Section 2.5, paragraph discussing Cayley-graph diameters and puzzle groups