  The pinwheel triangle of Conway and Radin is a standard example for tilings
with self-similarity and statistical circular symmetry. Many modifications were
constructed, all based on partitions of triangles or rectangles. The fractal
example of Frank and Whittaker requires 13 different types of tiles. We present
an example of a single tile with fractal boundary and very simple geometric
structure which has the same symmetry and spectral properties as the pinwheel
triangle.
