Polytopes of high rank for the alternating groups

DOI10.1016/j.jcta.2011.07.006zbMath1235.52021OpenAlexW2033249263MaRDI QIDQ645959

Maria Elisa Fernandes, Mark Mixer, Dimitri Leemans

Publication date: 11 November 2011

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.2011.07.006

zbMATH Keywords

polytopesalternating groupsregular actionCPR graphs

Mathematics Subject Classification ID

(n)-dimensional polytopes (52B11) Finite automorphism groups of algebraic, geometric, or combinatorial structures (20B25)

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Uses Software

• Magma

Cites Work

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• On arranging regular incidence-complexes as faces of higher-dimensional ones
• An atlas of abstract regular polytopes for small groups
• Reflection groups and polytopes over finite fields. III.
• A new Petrie-like construction for abstract polytopes
• Extensions of dually bipartite regular polytopes
• Extensions of regular polytopes with preassigned Schläfli symbol
• Reguläre Inzidenzkomplexe. II
• Diagrams for geometries and groups
• Buildings of spherical type and finite BN-pairs
• The Magma algebra system. I: The user language
• Realizations of regular toroidal maps of type \(\{4,4\}\)
• Reguläre Inzidenzkomplexe. I
• Higher toroidal regular polytopes
• Cyclotomic integers, nondiscrete tessellations, and quasicrystals
• Reflection groups and polytopes over finite fields. II.
• CPR graphs and regular polytopes
• An atlas of small regular abstract polytopes
• Problems on polytopes, their groups, and realizations
• Polytopes with groups of type PGL_2(q)
• Pseudo-real Riemann surfaces and chiral regular maps
• Generators for Alternating and Symmetric Groups
• MORE ON GENERATORS FOR ALTERNATING AND SYMMETRIC GROUPS
• Abstract Regular Polytopes
• REGULAR HYPERMAPS OVER PROJECTIVE LINEAR GROUPS
• Groups of type L ₂(q) acting on polytopes