Cayley extensions of maniplexes and polytopes
Date:
Contributed talk in the 10th Slovenian Conference on Graph Theory
Hotel Kompas, Kranjska Gora
Kranjska Gora, Slovenia
Abstract: A map on a surface whose automorphism group has a subgroup acting regularly on its vertices is called a Cayley map. Cayley extensions are a generalisation of that notion to maniplexes and polytopes. We define M to be a Cayley extension of K if the facets of M are isomorphic to K and if some subgroup of the automorphism group of M acts regularly on the facets of M. We will show that many natural extensions in the literature on maniplexes and polytopes are in fact Cayley extensions. We will also describe several universal Cayley extensions and examine the possibilities for their symmetry type graph.