Structural Chemistry

, Volume 13, Issue 3–4, pp 247–257 | Cite as

The Orbifold Notation for Two-Dimensional Groups

  • John H. Conway
  • Daniel H. Huson


This paper gives a detailed introduction to the orbifold notation for two-dimensional (2-D) symmetry groups. It discusses the correspondence between properties of orbifolds and symmetries in the original surface. The problem of determining a group in situ is addressed. Elementary proofs of the classification of the Euclidean and spherical 2-D symmetry groups are presented.

Symmetry group notation classification two-dimensional 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Conway, J. In Groups, Combinatorics and Geometry; Cambridge University Press: Cambridge, 1992; pp. 438-447 (London Mathematical Society Lecture Note Series 165).Google Scholar
  2. 2.
    Conway, J.; Delgado Friedrichs, O.; Huson, D.; Thurston, W. Contrib. Geometry Algebra 2001, 42, 475.Google Scholar
  3. 3.
    Coxeter, H.; Moser, W. Generators and Relations for Discrete Groups (Springer: Berlin, 1980).Google Scholar
  4. 4.
    Macbeath, A. Canad. J. Math. 1967, 19, 1192.Google Scholar
  5. 5.
    Schattschneider, D. Visions of Symmetry: Notebooks, Periodic Drawings and Related Work of M. C. Escher (Freeman: San Francisco, CA, 1990).Google Scholar
  6. 6.
    Thurston, W. The Geometry and Topology of Three-Manifolds (Princeton University: Princeton, New Jersey, 1980).Google Scholar

Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • John H. Conway
    • 1
  • Daniel H. Huson
    • 2
  1. 1.Department of MathematicsPrinceton UniversityPrinceton
  2. 2.WSI-InformatikUniversität TübingenTübingenGermany

Personalised recommendations