A construction of higher rank chiral polytopes

DOI10.1016/j.disc.2009.11.034zbMath1193.51024OpenAlexW2159437978MaRDI QIDQ966020

Daniel Pellicer

Publication date: 27 April 2010

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.disc.2009.11.034

zbMATH Keywords

rankregular polytopechiral polytopeGPR graph

Mathematics Subject Classification ID

Polyhedra and polytopes; regular figures, division of spaces (51M20)

Related Items (21)

Rotary one-facet maniplexes ⋮ Non-flat regular polytopes and restrictions on chiral polytopes ⋮ Symmetries of equivelar 4-toroids ⋮ More on chiral polytopes of type \(\{4,4,\dots,4\}\) with solvable automorphism groups ⋮ Construction of chiral 4-polytopes with alternating or symmetric automorphism group ⋮ All polytopes are coset geometries: characterizing automorphism groups of \(k\)-orbit abstract polytopes ⋮ Chiral polytopes whose smallest regular cover is a polytope ⋮ Constructing self-dual chiral polytopes ⋮ Rank 4 toroidal hypertopes ⋮ Two infinite families of chiral polytopes of type {4,4,4} with solvable automorphism groups ⋮ On the Schläfli symbol of chiral extensions of polytopes ⋮ Mixing and monodromy of abstract polytopes ⋮ Open problems on \(k\)-orbit polytopes ⋮ Abelian covers of chiral polytopes ⋮ An existence result on two-orbit maniplexes ⋮ Mixing chiral polytopes ⋮ Chiral extensions of chiral polytopes ⋮ Tight chiral polytopes ⋮ Some simplifications of the intersection condition of chiral form for polytopes ⋮ Hereditary Polytopes ⋮ Proper locally spherical hypertopes of hyperbolic type

Uses Software

• GAP

Cites Work

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• On arranging regular incidence-complexes as faces of higher-dimensional ones
• Extensions of regular polytopes with preassigned Schläfli symbol
• All polytopes are quotients, and isomorphic polytopes are quotients by conjugate subgroups
• Chirality and projective linear groups
• CPR graphs and regular polytopes
• Monodromy Groups and Self-Invariance
• Abstract Regular Polytopes
• Free Extensions of Chiral Polytopes
• Constructions for chiral polytopes

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