## Generalized Ammann tiling

The following set of pieces show how the Ammann tiling has three degrees of freedom.

PDF version

This shows the transformation rule for an Ammann
tiling using arbitrary rhombs, all sides unit length, with 3 degrees of freedom
in arbitrary angles a, b, and c all >0, and d=pi-a-b-c. The designs rotate
but cannot flip over (so the black-tipped pieces have no symmetry).

PDF version

If a=b=c, then the b tile expands with straight edges. If b=2*pi/k for
integer k, this tile rotates k-fold around a vertex to produce a k-fold tiling
of the plane, for any integer k.

Originally posted at pinterest.

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*Copyright
2015-2016 by Jim Millar *