A Pentagonal Crystal, the Golden Section, Alcove Packing and Aperiodic Tilings
نویسنده
چکیده
A Lie theoretic interpretation is given to a pattern with five-fold symmetry occurring in aperiodic Penrose tiling based on isosceles triangles with length ratios equal to the Golden Section. Specifically a B(∞) crystal based on that of Kashiwara is constructed exhibiting this five-fold symmetry. It is shown that it can be represented as a Kashiwara B(∞) crystal in type A4. Similar crystals with (2n+1)-fold symmetry are represented as Kashiwara crystals in type A2n. The weight diagrams of the latter inspire higher aperiodic tiling. In another approach alcove packing is seen to give aperiodic tiling in type A4. Finally 2m-fold symmetry is related to type Bm.
منابع مشابه
Aperiodic Tilings by Right Triangles
Let ψ denote the square root of the golden ratio, ψ = √
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