Hyperbolic Pyritohedra Constructed from the Coxeter Group [4,3,5]

  • Peter Lorimer
Part of the Mathematics and Its Applications book series (MAIA, volume 325)


Oriented closed hyperbolic orbifolds are constructed from the Coxeter group [4,3,5]. There are fifty-four of them. Each can be obtained from a hyperbolic pyritohedron by identifying pairs of its faces.


Fundamental Group Hyperbolic Space Quotient Group Coxeter Group Orbit Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    M. A. Armstrong, The fundamental group of the orbit space of a discontinuous group, Proc. Camb. Phil. Soc. 64 (1968), 299–301.zbMATHCrossRefGoogle Scholar
  2. [2]
    H. S. M. Coxeter, Regular honeycombs in hyperbolic space, Proceedings International Congress of Mathematicians, Amsterdam, III (1954), 154–169.Google Scholar
  3. [3]
    B. Maskit, On Poincaré’s theorem for fundamental polygons, Adv. in Math. 7 (1971), 219–230.CrossRefGoogle Scholar
  4. [4]
    J. M. Montesinos, Classical Tessellations and Three-Manifolds, Berlin: Springer, 1987.zbMATHCrossRefGoogle Scholar
  5. [5]
    J. Stillwell, Topology and Combinatorial Group Theory, New York: Springer, 1980.zbMATHCrossRefGoogle Scholar
  6. [6]
    W. Thurston, The geometry and topology of three-manifolds,Princeton: Princeton University Press, to appear.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1995

Authors and Affiliations

  • Peter Lorimer
    • 1
  1. 1.Department of MathematicsUniversity of AucklandAucklandNew Zealand

Personalised recommendations