The quaquaversal tiling is a nonperiodic tiling

Aperiodic tiling

An aperiodic tiling is a tiling obtained from an aperiodic set of tiles. Properly speaking, aperiodicity is a property of particular sets of tiles; any given finite tiling is either periodic or non-periodic...

 of the euclidean 3-space introduced by John Conway and Charles Radin. The basic solid tiles are half prisms arranged in a pattern which relies essentially on their previous construct, the pinwheel tiling

Pinwheel tiling

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 orientations....

. 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.

External links

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