Quasi regular polygons and their duals with Coxeter symmetries D n represented by complex numbers

M. Koca, N. O. Koca

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

This paper deals with tiling of the plane by quasi regular polygons and their duals. The problem is motivated from the fact that the graphene, infinite number of carbon molecules forming a honeycomb lattice, may have states with two bond lengths and equal bond angles or one bond length and different bond angles. We prove that the Euclidean plane can be tiled with two tiles consisting of quasi regular hexagons with two different lengths (isogonal hexagons) and regular hexagons. The dual lattice is constructed with the isotoxal hexagons (equal edges but two different interior angles) and regular hexagons. We also give similar tilings of the plane with the quasi regular polygons along with the regular polygons possessing the Coxeter symmetries Dn, n=2,3,4,5. The group elements as well as the vertices of the polygons are represented by the complex numbers.

Original languageEnglish
Article number012039
JournalJournal of Physics: Conference Series
Volume284
Issue number1
DOIs
Publication statusPublished - 2011

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complex numbers
polygons
hexagons
symmetry
tiles
graphene
apexes
carbon
molecules

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Quasi regular polygons and their duals with Coxeter symmetries D n represented by complex numbers. / Koca, M.; Koca, N. O.

In: Journal of Physics: Conference Series, Vol. 284, No. 1, 012039, 2011.

Research output: Contribution to journalArticle

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