Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
Conway, J. In Groups, Combinatorics and Geometry; Cambridge University Press: Cambridge, 1992; pp. 438-447 (London Mathematical Society Lecture Note Series 165).
Conway, J.; Delgado Friedrichs, O.; Huson, D.; Thurston, W. Contrib. Geometry Algebra 2001, 42, 475.
Coxeter, H.; Moser, W. Generators and Relations for Discrete Groups (Springer: Berlin, 1980).
Macbeath, A. Canad. J. Math. 1967, 19, 1192.
Schattschneider, D. Visions of Symmetry: Notebooks, Periodic Drawings and Related Work of M. C. Escher (Freeman: San Francisco, CA, 1990).
Thurston, W. The Geometry and Topology of Three-Manifolds (Princeton University: Princeton, New Jersey, 1980).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Conway, J.H., Huson, D.H. The Orbifold Notation for Two-Dimensional Groups. Structural Chemistry 13, 247–257 (2002). https://doi.org/10.1023/A:1015851621002
Issue Date:
DOI: https://doi.org/10.1023/A:1015851621002