Ammann Chair

Discovered by

Info

One of the tilings discovered by R. Ammann in 1977, published in [GS87] . The other ones (published there) are Ammann A3, Ammann A4, and Ammann A5 (better known as Ammann Beenker). The inflation factor of this substitution is quite small. It is the square root of the golden ratio, approx 1.272. These tilings are the dual tilings of the golden triangle tilings. The matching rules for the Ammann chair tilings can be expressed by using Ammann bars. The tiles are rep-tiles in a more general sense: For instance, each of the two tiles - say, T - can be dissected into similar copies of T, but of different sizes.

Substitution Rule

Rule Ammann Chair

Patch

Patch Ammann Chair

References

[GS87]
Gr├╝nbaum, B and Shephard, G.C.
Tilings and Patterns
W.H. Freeman 1987, MR0857454