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Twisted Honeycombs

About this Title

H. S. M. Coxeter

Publication: CBMS Regional Conference Series in Mathematics
Publication Year: 1970; Volume 4
ISBNs: 978-0-8218-4941-5 (print); 978-1-4704-2364-3 (online)
DOI: https://doi.org/10.1090/cbms/004

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Table of Contents

Front/Back Matter

Chapters

  • Introduction
  • Regular tessellations
  • Finite groups of rotations
  • Groups generated by two or three reflections
  • The Petrie polygon of a tessellation
  • The regular tessellations $\{p, q\}_r$
  • Three-dimensional honeycombs
  • The simplex, cube, cross polytope and 24-cell
  • The 120-cell and the 600-cell
  • Groups generated by four reflections
  • The Petrie polygon of a honeycomb
  • The regular honeycombs $\{p, q, r\}_t$
  • Finite groups of quaternions
  • Quaternions and Petrie polygons
  • Table 1. Regular tessellations $\{p, q\}_r$ and their groups
  • Table 2. Reflexible honeycombs and their groups
  • Table 3. Twisted honeycombs and their groups