Quaquaversal tiling

The quaquaversal tiling is a nonperiodic tiling of the euclidean 3-space introduced by John Conway and Charles Radin. The basic solid tiles are half prisms arranged in a pattern that relies essentially on their previous construct, the pinwheel tiling. The rotations relating these tiles belong to the group G(6,4) generated by two rotations of order 6 and 4 whose axes are perpendicular to each other. These rotations are dense in SO(3).

References

• "Quaquaversal tilings and rotations", Inventiones Mathematicae 132 (1): 179–188, 1998, doi:10.1007/s002220050221, Bibcode: 1998InMat.132..179C .
• "Subgroups of SO(3) associated with tilings", Journal of Algebra 202 (2): 611–633, 1998, doi:10.1006/jabr.1997.7320 .

External links

• A picture of a quaquaversal tiling
• Charles Radin page at the University of Texas