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The eighty-one types of isohedral tilings in the plane

Published online by Cambridge University Press:  24 October 2008

Branko Grünbaum  and
G. C. Shephard
Branko Grünbaum
Affiliation:
University of Washington, Seattle and University of British Columbia, Vancouver
G. C. Shephard
Affiliation:
University of Washington, Seattle and University of British Columbia, Vancouver
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Extract

1. A tiling is a collection = {Ti|i = 1, 2, …} of closed topological discs which covers the Euclidean plane E2, and of which the individual tiles Ti have disjoint interiors. We shall assume throughout that the intersection of any two tiles is a connected set. If each tile is congruent (directly or reflectively isometric) to a given set T, then the tiling is called monohedral and T is called the prototile of . Clearly every monohedral tiling is locally finite.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 82 , Issue 2 , September 1977 , pp. 177 - 196
Copyright
Copyright © Cambridge Philosophical Society 1977

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