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Angels and Devils

  • H. S. M. Coxeter

Abstract

About forty years ago, Abraham Sinkov and I wrote twin papers on the subject of groups determined by the periods of two generators S, T and of their commutator S -1 T -1 ST [Coxeter 1936; Sinkov 1936], never dreaming that twenty years later M. C. Escher would be using such groups (unconsciously) as symmetry groups for a carved ball and four other works of art [Escher 1971, Figures 112, 115, 226, 235, 244, 247; MacGillavry 1976, p. 18]. Those works have been reproduced here by kind permission of the Escher Foundation, Haags Gemeentemuseum, The Hague.

Keywords

Symmetry Group Euclidean Plane Hyperbolic Plane Hyperbolic Group Hyperbolic Geometry 
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.

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References

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    Coxeter, H. S. M. 1936. The groups determined by the relations S l = T m = (S -1 T -1 ST)P = 1 Duke Math. Journal. 2: 61–73.CrossRefGoogle Scholar
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    Coxeter, H. S. M. 1964. Regular compound tessellations of the hyperbolic plane. Proc. Royal Soc. London A 278: 147–167.CrossRefGoogle Scholar
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    Coxeter, H. S. M. 1979. The non-Euclidean symmetry of Escher’s picture ‘Circle Limit III’. Leonardo 12: 19–25, 32.Google Scholar
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Copyright information

© Wadsworth International 1981

Authors and Affiliations

  • H. S. M. Coxeter
    • 1
  1. 1.University of TorontoCanada

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