The quaquaversal tiling is a nonperiodic tiling of the euclidean 3-space introduced by

John Conway John Horton Conway (26 December 1937 – 11 April 2020) was an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory. He also made contributions to many branches ...

and Charles Radin. The basic solid tiles are half prisms arranged in a pattern that relies essentially on their previous construct, the

pinwheel tiling In geometry, pinwheel tilings are non-periodic tilings defined by Charles Radin and based on a construction due to John Conway. They are the first known non-periodic tilings to each have the property that their tiles appear in infinitely many or ...

. 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) In mechanics and geometry, the 3D rotation group, often denoted SO(3), is the group of all rotations about the origin of three-dimensional Euclidean space \R^3 under the operation of composition. By definition, a rotation about the origin is a tr ...

References

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External links

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picture
of a quaquaversal tiling
Charles Radin
page at the University of Texas Discrete geometry Tessellation {{geometry-stub