Locally unitary groups and regular polytopes

DOI10.1016/S0196-8858(02)00001-5zbMath1021.51009MaRDI QIDQ1865250

Peter McMullen, Egon Schulte

Publication date: 26 March 2003

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

zbMATH Keywords

hermitian formcomplex reflection groupabstract regular polytopesCoxeter diagraminvolutory reflection

Mathematics Subject Classification ID

Reflection and Coxeter groups (group-theoretic aspects) (20F55) Polyhedra and polytopes; regular figures, division of spaces (51M20) Reflection groups, reflection geometries (51F15)

Cites Work

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• A census of regular 3-polystroma arising from honeycombs
• Hermitian forms and locally toroidal regular polytopes
• Incidence-polytopes of type \(\{ 6,3,3\}\)
• Incidence-polytopes with toroidal cells
• Regular 3-complexes with toroidal cells
• Signed graphs, root lattices, and Coxeter groups
• Chirality and projective linear groups
• Eisenstein integers and related \(C\)-groups
• Doubly transitive automorphism groups of combinatorial surfaces
• Polytopes related to the Picard group
• Higher toroidal regular polytopes
• Locally toroidal regular polytopes of rank 4
• Finite groups generated by unitary reflections
• Regular 4‐polytopes related to general orthogonal groups
• Groups Generated by Unitary Reflections of Period Two
• Abstract Definitions for Reflection Groups
• An Infinite Graph of Girth 12
• Finite complex reflection groups
• 3-Pseudomanifolds with Preassigned Links
• Abstract Regular Polytopes
• Twisted Groups and Locally Toroidal Regular Polytopes
• RINGS OF DEFINITION OF DENSE SUBGROUPS OF SEMISIMPLE LINEAR GROUPS
• Regular Complex Polytopes
• Unitary Groups Generated by Reflections
• Finite Unitary Reflection Groups

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