In [RaSa98] Radin and Sadun constructed 3-dimensional tilings associated with subgroups of SO(3) generated by two rational rotations. One of the tilings was called “dite and kart”. The two-dimensional corresponding tiling is shown here (taken from Fig 1 in [RaSa98]).
This substitution tiling is the example of substitution tilings with infinite rotations. Its statistical and dynamical properties were studied in several papers by C. Radin, see for instance [Rad92] , [Rad97] . In particular, it was shown that the orientations of triangles in the pinwheel tiling are equally distributed in the circle. Despite the occurrance of irrational edge lengths and incommensurate angles, all vertices of the pinwheel tiling have rational coordinates.
With Decoration Finite Local Complexity Saduns Generalised Pinwheels Polytopal Tiles Self Similar Substitution Mld Class Pinwheel