Generalization of Rubik’s cube group to n-dimensional case

Abstract

In this paper, Rubik’s cube group in [Formula: see text]-dimensional case is described. In that case, some interesting effects arise, which is related with angular rotations. For [Formula: see text], the group [Formula: see text] arises, which can be realized as a factor group of [Formula: see text] by commutation [Formula: see text]. For [Formula: see text] there are no such effects, because corresponding factor is trivial. Rubik’s cube is an important model to study effects of groups related with, in particular, holonomy groups from differential geometry.