• DOI:10.1090/CONM/764/15359
• Corpus ID: 119590761

Prescribing symmetries and automorphisms for polytopes

@article{Schulte2019PrescribingSA,
  title={Prescribing symmetries and automorphisms for
 polytopes},
  author={Egon Schulte and Pablo Sober'on and Gordon I. Williams},
  journal={arXiv: Combinatorics},
  year={2019}
}

• E. Schulte, P. Sober'on, Gordon I. Williams
• Published 14 February 2019
• Mathematics
• arXiv: Combinatorics

We study finite groups that occur as combinatorial automorphism groups or geometric symmetry groups of convex polytopes. When $\Gamma$ is a subgroup of the combinatorial automorphism group of a convex $d$-polytope, $d\geq 3$, then there exists a convex $d$-polytope related to the original polytope with combinatorial automorphism group exactly $\Gamma$. When $\Gamma$ is a subgroup of the geometric symmetry group of a convex $d$-polytope, $d\geq 3$, then there exists a convex $d$-polytope related to the original polytope with both geometric symmetry group and combinatorial automorphism group exactly $\Gamma$. These symmetry-breaking results then are applied to show that for every abelian group $\Gamma$ of even order and every involution $\sigma$ of $\Gamma$, there is a centrally symmetric convex polytope with geometric symmetry group $\Gamma$ such that $\sigma$ corresponds to the central symmetry.