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.


Euclidean Space Dimensional Euclidean Space Orthogonal Axis Triangular Prism Repeated Rotation 
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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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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