Vertex-Faithful Regular Polyhedra
Combinatorics
2020-06-01 v1 Group Theory
Abstract
We study the abstract regular polyhedra with automorphism groups that act faithfully on their vertices, and show that each non-flat abstract regular polyhedron covers a "vertex-faithful" polyhedron with the same number of vertices. We then use this result and earlier work on flat polyhedra to study abstract regular polyhedra based on the size of their vertex set. In particular, we classify all regular polyhedra where the number of vertices is prime or twice a prime. We also construct the smallest regular polyhedra with a prime squared number of vertices.
Keywords
Cite
@article{arxiv.2005.14252,
title = {Vertex-Faithful Regular Polyhedra},
author = {Gabe Cunningham and Mark Mixer},
journal= {arXiv preprint arXiv:2005.14252},
year = {2020}
}