The Geometry Junkyard

Penrose Tiles

Penrose was not the first to discover aperiodic tilings, but his is probably the most well-known. In its simplest form, it consists of 36- and 72-degree rhombi, with "matching rules" forcing the rhombi to line up against each other only in certain patterns. It can also be formed by tiles in the shape of "kites" and "darts" or even by deformed chickens (see the "perplexing poultry" entry below). Part of the interest in this tiling stems from the fact that it has a five-fold symmetry impossible in periodic crystals, and has been used to explain the structure of certain "quasicrystal" substances.

From the Geometry Junkyard, computational and recreational geometry pointers.
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David Eppstein, Theory Group, ICS, UC Irvine.
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