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The Heesch number of a shape is the maximum number of layers of copies of the same shape that can surround it. For example the following shape (in the center) has a Heesch number of 4, because we can get at most 4 layers to surround it:

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Given a shape, is there an efficient algorithm to compute its Heesch number? The only thing I can think of is to do a brute-force BFS search, surrounding it layer by layer. But this seems awfully inefficient.

Dmitry Kamenetsky
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1 Answers1

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Look at this paper

Casey Mann, and B. Charles Thomas (2016) Heesch Numbers of Edge-Marked Polyforms

In this article, the results of a computerized search for edge-marked polyforms (tiles formed from either equilateral triangles, squares, or regular hexagons) with finite Heesch number are presented.

Ivan Z
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