Open problems on k-orbit polytopes

2016/08/29 by Gabe Cunningham, Cunningham, Gabe, Daniel Pellicer +1
Engineering · Mathematics · Computer Science · #graph theory and CDMA systems #Advanced Combinatorial Mathematics #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1608.07993

Abstract

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 implicitly in previous work but has not been formalized before.

Related

• Orbit graphs and face-transitivity of k-orbit polytopes
• Problems on Polytopes, Their Groups, and Realizations
• All polytopes are coset geometries: characterizing automorphism groups of k-orbit abstract polytopes
• Some Algorithmic Problems in Polytope Theory
• On the Size of Equifacetted Semi-Regular Polytopes