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

作者：Doignon Jean-Paul^*

来源：Discrete & Computational Geometry, 2018, 59(2): 451-460.

DOI：10.1007/s00454-017-9945-0

• Automorphism
• Group
• Graph
• Convex polytope

For any given finite group, Schulte and Williams (Discrete Comput Geom 54(2):444-458, 2015) establish the existence of 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 (J Combin Theory Ser B 31(3):297-312, 1981); the diameter of its skeleton is at most 2; any combinatorial automorphism of the polytope is induced by some isometry of the space; any automorphism of the skeleton is a combinatorial automorphism.

• 出版日期2018-3