Discrete Groups Generated by Reflections

TLDR

The paper studies polytopes with restricted dihedral angles, their fundamental regions, and provides an abstract definition. The authors enumerate all irreducible reflection groups via continued products of generators and a two‑operation generation scheme. They report the total number of reflections and present a table and graphical representation of all irreducible finite reflection groups in elliptic space. Sections 1–3 discuss the central inversion.

Abstract

1-3. Polytopes with restricted dihedral angles 590 4-7. Fundamental regions 594 8. The abstract definition 599 9. Complete enumeration of the irreducible groups 601 10-13. Continued products of the generators 602 14, 15. The central inversion 606 16. The total number of reflections 610 17. Generation by two operations 612 18. Elliptic space 617 Table of irreducible finite groups generated by reflections 618 Graphical representation 619 Index 620 References 620