Abstract
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 B m .
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