Abstract
Consider a hypergraph nd where the vertices are points of the d-dimensional cube [n]d and the edges are all sets of n points such that they are in one line. We study the structure of the group of automorphisms of nd, i.e., permutations of points of [n]d preserving the edges. In this paper we provide a complete characterization. Moreover, we consider the Colored Cube Isomorphism problem of deciding whether for two colorings of the vertices of nd there exists an automorphism of nd preserving the colors. We show that this problem is GI-complete. 33A preliminary version of this work appeared in the proceedings of Computing and Combinatorics — 22nd International Conference, COCOON 2016.
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