2 citations · 2 across the 5 of their papers we have counts for
6 papers
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…
Hereditary Polytopes
Mark Mixer, Egon Schulte, Asia Ivic Weiss
Every regular polytope has the remarkable property that it inherits all symmetries of each of its facets. This property distinguishes a natural class of polytopes which are called…
On the Size of Equifacetted Semi-Regular Polytopes
Tomaz Pisanski, Egon Schulte, Asia Ivic Weiss
Unlike the situation in the classical theory of convex polytopes, there is a wealth of semi-regular abstract polytopes, including interesting examples exhibiting some unexpected ph…
Problems on Polytopes, Their Groups, and Realizations
Egon Schulte, Asia Ivic Weiss
The paper gives a collection of open problems on abstract polytopes that were either presented at the Polytopes Day in Calgary or motivated by discussions at the preceding Workshop…
Semisymmetric Graphs from Polytopes
Barry Monson, Tomaz Pisanski, Egon Schulte +1
Every finite, self-dual, regular (or chiral) 4-polytope of type {3,q,3} has a trivalent 3-transitive (or 2-transitive) medial layer graph. Here, by dropping self-duality, we obtain…
Petrie-Coxeter Maps Revisited
Isabel Hubard, Egon Schulte, Asia Ivic Weiss
This paper presents a technique for constructing new chiral or regular polyhedra (or maps) from self-dual abstract chiral polytopes of rank 4. From improperly self-dual chiral poly…