DOAJ Open Access 2015

Symmetries of Monocoronal Tilings

Dirk Frettlöh Alexey Garber

Lihat Sumber DOI

Abstrak

The vertex corona of a vertex of some tiling is the vertex together with the adjacent tiles. A tiling where all vertex coronae are congruent is called monocoronal. We provide a classification of monocoronal tilings in the Euclidean plane and derive a list of all possible symmetry groups of monocoronal tilings. In particular, any monocoronal tiling with respect to direct congruence is crystallographic, whereas any monocoronal tiling with respect to congruence (reflections allowed) is either crystallographic or it has a one-dimensional translation group. Furthermore, bounds on the number of the dimensions of the translation group of monocoronal tilings in higher dimensional Euclidean space are obtained.

Topik & Kata Kunci

Mathematics

Penulis (2)

Dirk Frettlöh

Alexey Garber

Format Sitasi

APA MLA BibTeX

Frettlöh, D., Garber, A. (2015). Symmetries of Monocoronal Tilings. https://doi.org/10.46298/dmtcs.2142

Akses Cepat

Lihat di Sumber doi.org/10.46298/dmtcs.2142

Informasi Jurnal

Tahun Terbit: 2015
Sumber Database: DOAJ
DOI: 10.46298/dmtcs.2142
Akses: Open Access ✓