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.


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.


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



[1] C. S. Kaplan, "Heesch Numbers of Unmarked Polyforms."


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