Inventiones mathematicae

, Volume 132, Issue 1, pp 179–188 | Cite as

Quaquaversal tilings and rotations

  • John H. Conway
  • Charles Radin


We construct a hierarchical tiling of 3 dimensional Euclidean space based on a triangular prism, using repeated rotations, about orthogonal axes, by angles 2π/m and 2π/n. To analyze the structure of the tiling we are led to determine the group G(m,n) generated by such a pair of rotations, for m=n=3 and for m=3, n=4.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • John H. Conway
    • 1
  • Charles Radin
    • 2
  1. 1.Department of Mathematics, Princeton University, Princeton, NJ 08544, USAUS
  2. 2.Department of Mathematics, University of Texas, Austin, TX 78712, USAUS

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