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Constructions of Chiral Polytopes of Small Rank

Published:2011-06-25
Printed: Dec 2011
• Antonio Breda D'Azevedo,
Departamento de Matemática, Universidade de Aveiro, P 3800 Aveiro, Portugal
• Gareth A. Jones,
School of Mathematics, University of Southampton, Southampton SO17 1BJ, United Kingdom
• Egon Schulte,
Department of Mathematics, Northeastern University, Boston, Massachusetts, USA, 02115
 Format: LaTeX MathJax

Abstract

An abstract polytope of rank $n$ is said to be chiral if its automorphism group has precisely two orbits on the flags, such that adjacent flags belong to distinct orbits. This paper describes a general method for deriving new finite chiral polytopes from old finite chiral polytopes of the same rank. In particular, the technique is used to construct many new examples in ranks $3$, $4$, and $5$.
 Keywords: abstract regular polytope, chiral polytope, chiral maps
 MSC Classifications: 51M20 - Polyhedra and polytopes; regular figures, division of spaces [See also 51F15] 52B15 - Symmetry properties of polytopes 05C25 - Graphs and abstract algebra (groups, rings, fields, etc.) [See also 20F65]

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