Isohedral simple tilings: Binodal and by tiles with ≤16 faces

Olaf Delgado-Friedrichs; Michael O'Keeffe

doi:10.1107/S0108767305009578

Isohedral simple tilings: Binodal and by tiles with ≤16 faces

Olaf Delgado-Friedrichs
, Michael O'Keeffe^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

43 Citations (Scopus)

Abstract

All isohedral simple tilings of 3D Euclidian space by tiles with ≤16 faces have been determined. There are no such tilings by polyhedra with less than 14 faces. For simple polyhedra with 14, 15 and 16 faces, there are respectively 10, 65 and 434 that fill space and a total of 23, 136 and 710 distinct tilings. The tilings by 14-face polyhedra are described in detail as are binodal (vertex 2-transitive) isohedral simple tilings.

Original language	English
Pages (from-to)	358-362
Number of pages	5
Journal	Acta Crystallographica Section A: Foundations of Crystallography
Volume	61
Issue number	3
DOIs	https://doi.org/10.1107/S0108767305009578
Publication status	Published - May 2005
Externally published	Yes

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abstract = "All isohedral simple tilings of 3D Euclidian space by tiles with ≤16 faces have been determined. There are no such tilings by polyhedra with less than 14 faces. For simple polyhedra with 14, 15 and 16 faces, there are respectively 10, 65 and 434 that fill space and a total of 23, 136 and 710 distinct tilings. The tilings by 14-face polyhedra are described in detail as are binodal (vertex 2-transitive) isohedral simple tilings.",

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AB - All isohedral simple tilings of 3D Euclidian space by tiles with ≤16 faces have been determined. There are no such tilings by polyhedra with less than 14 faces. For simple polyhedra with 14, 15 and 16 faces, there are respectively 10, 65 and 434 that fill space and a total of 23, 136 and 710 distinct tilings. The tilings by 14-face polyhedra are described in detail as are binodal (vertex 2-transitive) isohedral simple tilings.

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Isohedral simple tilings: Binodal and by tiles with ≤16 faces

Abstract

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