3 papers
math.CO2019
Prescribing Symmetries and Automorphisms for Polytopes
Egon Schulte, Pablo Soberón, Gordon Ian Williams
We study finite groups that occur as combinatorial automorphism groups or geometric symmetry groups of convex polytopes. When is a subgroup of the combinatorial automorphism gr…
math.CO2015
Polytopes with Preassigned Automorphism Groups
Egon Schulte, Gordon Ian Williams
We prove that every finite group is the automorphism group of a finite abstract polytope isomorphic to a face-to-face tessellation of a sphere by topological copies of convex polyt…
math.CO2009
Representing the Sporadic Archimedean Polyhedra as Abstract Polytopes
Michael Hartley, Gordon Williams
We present the results of an investigation into the representations of Archimedean polyhedra (those polyhedra containing only one type of vertex figure) as quotients of regular abs…