TY - JOUR
T1 - Quasi regular polygons and their duals with Coxeter symmetries D n represented by complex numbers
AU - Koca, M.
AU - Koca, N. O.
PY - 2011
Y1 - 2011
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=80052061096&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=80052061096&partnerID=8YFLogxK
U2 - 10.1088/1742-6596/284/1/012039
DO - 10.1088/1742-6596/284/1/012039
M3 - Article
AN - SCOPUS:80052061096
SN - 1742-6588
VL - 284
JO - Journal of Physics: Conference Series
JF - Journal of Physics: Conference Series
IS - 1
M1 - 012039
ER -