Combinatorial d-tori with a large symmetry group (Q1096889)

The zonotope which is the vector sum of the \(d+1\) segments joining the centroid of a regular d-simplex to its vertices tiles E d by translation. The authors show here that a suitable triangulation of it extends to a triangulation of E d, which under identification by certain translations yields a triangulation of the d-torus with \(n=2^{d+1}-1\) vertices and an automorphism group of order \(2(d+1)n\) acting transitively on the vertices. The case \(d=2\) is the well-known Czászár torus.