8 citations · 27 across the 13 of their papers we have counts for
18 papers
Maniplexes as a Foundation for Cross-Linked Databases of Symmetric Objects
Katja Berčič, Gabe Cunningham, Andrés David Santamaría-Galvis +1
Graphs, maps on surfaces, and abstract polytopes are related combinatorial structures that tend to be studied by different communities using their own tools and databases. Maniplex…
Representing alternating groups as self-dual string C-groups of high rank
Gabe Cunningham, Mark Mixer
The highest rank of a string C-group representation of the alternating group is known for each , but no self-dual representations attaining this highest rank are known whe…
Cayley extensions of maniplexes and polytopes
Gabe Cunningham, Elías Mochán, Antonio Montero
A map on a surface whose automorphism group has a subgroup acting regularly on its vertices is called a Cayley map. Here we generalize that notion to maniplexes and polytopes. We d…
Tight Chiral Polytopes
Gabe Cunningham, Daniel Pellicer
A chiral polytope with Schläfli symbol has at least flags, and it is called \emph{tight} if the number of flags meets this lower bo…
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…
Flat extensions of abstract polytopes
Gabe Cunningham
We consider the problem of constructing an abstract -polytope with facets isomorphic to a given -polytope , where . In particular, we consider the ca…