Gabe Cunningham

collaborators

4 papers

math.CO2020

Tight Chiral Polytopes

Gabe Cunningham, Daniel Pellicer

A chiral polytope with Schläfli symbol ${p_{1}, \dots, p_{n - 1}}$ has at least $2 p_{1} \dots p_{n - 1}$ flags, and it is called \emph{tight} if the number of flags meets this lower bo…

math.CO2020

Vertex-Faithful Regular Polyhedra

Gabe Cunningham, Mark Mixer

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-fai…

math.CO2020

Flat extensions of abstract polytopes

Gabe Cunningham

We consider the problem of constructing an abstract $(n + 1)$ -polytope $Q$ with $k$ facets isomorphic to a given $n$ -polytope $P$ , where $k \geq 3$ . In particular, we consider the ca…

math.CO2017

Non-flat regular polytopes and restrictions on chiral polytopes

Gabe Cunningham

An abstract polytope is \emph{flat} if every facet is incident on every vertex. In this paper, we prove that no chiral polytope has flat finite regular facets and finite regular ve…