Equivelar toroids with few flag-orbits
Date:
Contributed talk in the Conference Symmetries and Covers of Discrete Objects
Rydges Lakeland Resort
Queenstown, New Zealand
Abstract: An $(n+1)$-toroid is a quotient of a tessellation of the $n$-dimensional euclidean space with a lattice group. Toroids are generalizations of maps in the torus on higher dimensions and also provide examples of abstract polytopes. Equivelar maps in the $2$-torus ($3$-toroids) where classified by Brehem and Kühnel in 2008. In 2012 Hubard, Orbanić, Pellicer and Weiss classified equivelar $4$-toroids. However, a complete classification for any dimension seems to be a very hard problem. In the talk we will present a classification of equivelar $(n+1)$-toroids with less than $n$ flag-orbits; in particular, we will discuss a classification of $2$-orbit toroids of arbitrary dimension.