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Patterns on the 2-Sphere

Published online by Cambridge University Press:  26 February 2010

Branko Grünbaum  and
G. C. Shephard
Branko Grünbaum
Affiliation:
University of Washington, Seattle, Wa 98195, U.S.A.
G. C. Shephard
Affiliation:
University of East Anglia, Norwich NR4 7TJ, England.
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Extract

Problems of classifying and enumerating types of plane patterns, tilings, and other repeating geometrical structures have interested mathematicians, crystallographers and others for many years. Recently we have formulated the general principles that seem to underlie many of the published treatments of these topics, and so have been able to put on a mathematical basis classification criteria often justified mainly on intuitive grounds. In other words, we can now decide whether or not two given patterns are of the same “type”, at one of a number of different possible levels of classification, without relying on some vaguely expressed distinction based on a “feeling” as to whether the objects in question should be regarded as of distinguishable kinds, or not.

Type
Research Article
Information
Mathematika , Volume 28 , Issue 1 , June 1981 , pp. 1 - 35
Copyright
Copyright © University College London 1981

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