The intersection condition for regular polytopes

DOI10.1016/j.jcta.2013.03.009zbMath1278.05053OpenAlexW2040543254MaRDI QIDQ388199

Deborah Oliveros, Marston D. E. Conder

Publication date: 19 December 2013

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcta.2013.03.009

zbMATH Keywords

Coxeter groupsregular mapsalternating groupsregular polytopesintersection propertypolytopal maps

Mathematics Subject Classification ID

Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) (52B05) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Combinatorial aspects of finite geometries (05B25)

Related Items (8)

Highly symmetric hypertopes ⋮ Projective linear groups as automorphism groups of chiral polytopes ⋮ Regular maps with an alternating or symmetric group as automorphism group ⋮ String C-group representations of alternating groups ⋮ Existence of regular 3-polytopes of order \(2^n\) ⋮ Some simplifications of the intersection condition of chiral form for polytopes ⋮ String C-group representations of almost simple groups: A survey ⋮ Unnamed Item

Uses Software

• Magma

Cites Work

• Regular maps with simple underlying graphs
• Polytopes of high rank for the alternating groups
• Polytopes of high rank for the symmetric groups
• An exploration of locally projective polytopes
• The genera, reflexibility and simplicity of regular maps
• Regular maps and hypermaps of Euler characteristic \(-1\) to \(-200\)
• The Magma algebra system. I: The user language
• On the number of abstract regular polytopes whose automorphism group is a Suzuki simple group \(Sz(q)\)
• Alternating quotients of Fuchsian groups
• CPR graphs and regular polytopes
• Modular Reduction in Abstract Polytopes
• Polytopes with groups of type PGL_2(q)
• MORE ON GENERATORS FOR ALTERNATING AND SYMMETRIC GROUPS
• Abstract Regular Polytopes
• Groups of type L ₂(q) acting on polytopes
• A Bound for the Number of Automorphisms of a Compact Riemann Surface
• On the Number of Automorphisms of a Closed Riemann Surface
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