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The Pegg Snakes Are Heesch-3 Tiles

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The first corona of a tile is a set of tiles congruent to that surrounds . If the first corona exists and can itself be surrounded by a set of tiles congruent to , that is called the second corona, and so on.

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A Heesch tile of order is a tile that has a corona of order , but not of order .

The Pegg snake is an infinite sequence of polyiamonds that are each a Heesch tile of order 3. They were found by Ed Pegg Jr and Craig Kaplan, who named them.

This shows that there are infinitely many Heesch tiles of order 3.

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Contributed by: Ed Pegg Jr and Craig Kaplan (June 13)
Open content licensed under CC BY-NC-SA

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Reference

[1] C. S. Kaplan, "Heesch Numbers of Unmarked Polyforms." arxiv.org/abs/2105.09438.

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