Any Finite Group is the Group of Some Binary, Convex Polytope

Jean-Paul Doignon

Published 2016-02-09Version 1

For any given finite group, Schulte and Williams (2015) produce a convex polytope whose combinatorial automorphisms form a group isomorphic to the given group. We provide here a shorter proof for a stronger result: the convex polytope we build for the given finite group is binary, and even combinatorial in the sense of Naddef and Pulleyblank (1981); the diameter of its skeleton is at most 2; any automorphism of the skeleton is a combinatorial automorphism; any combinatorial automorphism of the polytope is induced by some isometry of the space.