Comptes Rendus
The Heesch number for multiple prototiles is unbounded
Comptes Rendus. Mathématique, Volume 353 (2015) no. 8, pp. 665-669.

In this paper we show that, for all integers k3 and n1, there exists a protoset consisting of k prototiles, whose Heesch number is n. This disproves a conjecture by Grünbaum and Shephard.

Dans cette note, on prouve que, pour tous entiers k3 et n1, il existe un proto-ensemble qui possède k proto-pavés et dont le nombre de Heesch est égal à n. Cela réfute une conjecture de Grünbaum et Shephard.

Published online:
DOI: 10.1016/j.crma.2015.05.002

Bojan Bašić 1

1 Department of Mathematics and Informatics, University of Novi Sad, Trg Dositeja Obradovića 4, 21000 Novi Sad, Serbia
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     title = {The {Heesch} number for multiple prototiles is unbounded},
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     doi = {10.1016/j.crma.2015.05.002},
     language = {en},
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Bojan Bašić. The Heesch number for multiple prototiles is unbounded. Comptes Rendus. Mathématique, Volume 353 (2015) no. 8, pp. 665-669. doi : 10.1016/j.crma.2015.05.002.

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