Angels and Devils

  • H. S. M. Coxeter


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.


Symmetry Group Euclidean Plane Hyperbolic Plane Hyperbolic Group Hyperbolic Geometry 
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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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Copyright information

© Wadsworth International 1981

Authors and Affiliations

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

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