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Isohedrally compatible tilings. (English) Zbl 1016.52012

Summary: Two of the 17 (plane) crystallographic groups, \(G\) and \(H\), are isohedrally compatible if there exists a tile which admits separate tilings with respective automorphism groups \(G\) and \(H\). The purpose of this article is to show that of the 136 possible pairs, 77 are definitely compatible, 44 are not and we conjecture the remaining 15 pairs are also not compatible.

MSC:

52C20 Tilings in \(2\) dimensions (aspects of discrete geometry)
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