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- Title
Any Finite Group is the Group of Some Binary, Convex Polytope.
- Authors
Doignon, Jean-Paul
- Abstract
For any given finite group, Schulte and Williams (Discrete Comput Geom 54(2):444–458, <xref>2015</xref>) 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, <xref>1981</xref>); 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.
- Subjects
CONVEX polytopes; FINITE groups; COMBINATORICS; AUTOMORPHISMS; ISOMETRICS (Mathematics)
- Publication
Discrete & Computational Geometry, 2018, Vol 59, Issue 2, p451
- ISSN
0179-5376
- Publication type
Article
- DOI
10.1007/s00454-017-9945-0