The invariants of n-dimensional Rubik's Cube

TL;DR

This paper generalizes the n-dimensional Rubik's Cube, analyzes its group invariants, and describes all invariants for the puzzle in arbitrary dimensions, extending known properties to higher-dimensional cases.

Contribution

It provides a comprehensive description of all invariants of the n-dimensional Rubik's Cube, a significant extension of existing knowledge to higher dimensions.

Findings

Identified all invariants of the n-dimensional Rubik's Cube.

Generalized the concept of invariants to arbitrary dimensions.

Extended the understanding of the cube's group properties.

Abstract

It is well known that Rubik's cube has a set of group invariants. These values do not change if any layer was rotated, but they can change in case if some of the cubes were removed from the puzzle, mixed up and returned back. In this paper, we generalize the puzzle to the case of an arbitrary dimension after which we describe all the invariants.