Orbit graphs and face-transitivity of k-orbit polytopes

2012/12/12 by Gabe Cunningham, Cunningham, Gabe
Computer Science · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #math.CO #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1212.2937

This paper has been merged with another paper: see arXiv:1303.6802

openalex publication_date 2012/12/12 · arxiv created 2013/06/07 · arxiv updated 2013/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The orbit graph of a k-orbit polytope is a graph on k nodes that shows how the flag orbits are related by flag adjacency. Using orbit graphs, we classify k-orbit polytopes and determine when a k-orbit polytope is i-transitive. We then provide an explicit classification of three-orbit polytopes, and we describe a generating set for their automorphism groups.

Citations

• Finite Polytopes have Finite Regular Covers
• Symmetry Type Graphs of Abstract Polytopes and Maniplexes

Related

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• Symmetry Type Graphs of Abstract Polytopes and Maniplexes
• All polytopes are coset geometries: characterizing automorphism groups of k-orbit abstract polytopes
• Medial symmetry type graphs
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