8 citations · 17 across the 14 of their papers we have counts for
15 papers
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…
An existence result on two-orbit maniplexes
Daniel Pellicer, Primož Potočnik, Micael Toledo
A maniplex of rank n is a connected, n-valent, edge-coloured graph that generalises abstract polytopes and maps. If the automorphism group of a maniplex M partitions the vertex-set…
Open problems on k-orbit polytopes
Gabe Cunningham, Daniel Pellicer
We present 35 open problems on combinatorial, geometric and algebraic aspects of k-orbit abstract polytopes. We also present a theory of rooted polytopes that has appeared implicit…
Cubic Tessellations of the Helicosms
Isabel Hubard, Mark Mixer, Daniel Pellicer +1
Up to isomorphism there are six fixed-point free crystallographic groups in Euclidean Space generated by twists (screw motions). In each case, an orientable 3-manifold is obtained…
Classification of tight regular polyhedra
Gabe Cunningham, Daniel Pellicer
A regular polyhedron of type {p, q} has at least 2pq flags, and it is called tight if it has exactly 2pq flags. The values of p and q for which there exist tight orientably regular…
A finite chiral 4-polytope in
Javier Bracho, Isabel Hubard, Daniel Pellicer
In this paper, we give an example of a chiral 4-polytope in projective 3-space. This example naturally yields a finite chiral 4-polytope in Euclidean 4-space, giving a counterexamp…