Affinely regular integral simplices (Q1179592)

An integral simplex is a non-degenerate simplex of \(\mathbb{R}^ n\) with all vertices in \(\mathbb{Z}^ n\). The group of affine bijections of \(R^ n\) preserving \(\mathbb{Z}^ n\) is denoted \(\text{Aff} \mathbb{Z}^ n\). For an integral simplex \(S\), the author considers the subgroups of \(\text{Aff} \mathbb{Z}^ n\), which preserve \(S\). If this group is isomorphic to the permutation group of \(n+1\) objects, \(S\) is called affinely regular. The author gives a characterization of affinely regular integral simplices in terms of the divisors of \(n+1\).