4 citations · 4 across the 4 of their papers we have counts for
6 papers
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…
Graphs with obstacle number greater than one
Leah Wrenn Berman, Glenn G. Chappell, Jill R. Faudree +3
An \emph{obstacle representation} of a graph is a straight-line drawing of in the plane together with a collection of connected subsets of the plane, called \emph{obstacles…
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…
Minimal covers of the prisms and antiprisms
Michael I. Hartley, Daniel Pellicer, Gordon Williams
This paper contains a classication of the regular minimal abstract polytopes that act as covers for the convex polyhedral prisms and antiprisms. It includes a detailed discussion o…
Quotient Representations of Uniform Tilings
Gordon Williams, Daniel Pellicer
Given a flag in each of the vertex-transitive tessellations of the Euclidean plane by regular polygons, we determine the flag stabilizer under the action of the automorphism group…
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…