The smallest regular polytopes of given rank

DOI10.1016/j.aim.2012.12.015zbMath1273.51013OpenAlexW2078506869MaRDI QIDQ1944322

Marston D. E. Conder

Publication date: 5 April 2013

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

Full work available at URL: https://doi.org/10.1016/j.aim.2012.12.015

zbMATH Keywords

automorphism groupabstract polytoperegular polytopestring Coxeter grouptight polytope.

Mathematics Subject Classification ID

Finite automorphism groups of algebraic, geometric, or combinatorial structures (20B25) Polyhedra and polytopes; regular figures, division of spaces (51M20) Algebraic aspects of posets (06A11) Symmetry properties of polytopes (52B15) Group actions on combinatorial structures (05E18)

Related Items (17)

Rotary one-facet maniplexes ⋮ Classification of tight regular polyhedra ⋮ Stratified operations on maniplexes ⋮ Non-flat regular polytopes and restrictions on chiral polytopes ⋮ More on chiral polytopes of type \(\{4,4,\dots,4\}\) with solvable automorphism groups ⋮ String C-groups as transitive subgroups of \(\operatorname{S}_n\) ⋮ On regular polytopes of 2-power order ⋮ Polytopes of high rank for the symmetric groups ⋮ Mapification of n-dimensional abstract polytopes and hypertopes ⋮ Open problems on \(k\)-orbit polytopes ⋮ Abelian covers of chiral polytopes ⋮ Existence of regular 3-hypertopes with \(2^n\) chambers ⋮ An extension of the classification of high rank regular polytopes ⋮ String C-group representations of alternating groups ⋮ Tight chiral polytopes ⋮ Existence of regular 3-polytopes of order \(2^n\) ⋮ Some simplifications of the intersection condition of chiral form for polytopes

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