Generalized Ammann tiling

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

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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).

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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