Quasiregular rhombic tiling
- Quasiregular rhombic tiling
Infobox face-uniform tiling
Type=Dual semiregular tiling
Face_List=30-60 rhombus
Wythoff_Symbol=***
Symmetry_Group=p6m
or *632
Face_Type=V3.6.3.6
Dual=Trihexagonal_tiling
Property_List=edge-transitive face-transitive
In geometry, the quasiregular rhombic tiling is a tiling of identical 60° rhombi polygons on the Euclidean plane. There are two types of vertices, one with three rhombi and one with six rhombi.
Conway calls it a rhombille.
This is the dual of the trihexagonal tiling.
Related polyhedra and tilings
This tiling is topologically related as a part of sequence of polyhedra constructed from rhombic faces and face configurations of "V3.n.3.n". This set is called quasi-regular because there is only one type of face, with equal edge lengths, but they are not regular polygons. These vertex-transitive figures have (*n32) reflectional symmetry.
ee also
* Tilings of regular polygons
References
* John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, "The Symmetry of Things" 2008, ISBN 978-1-56881-220-5 [http://www.akpeters.com/product.asp?ProdCode=2205]
* (Chapter 2.1: "Regular and uniform tilings", p.58-65)
* Williams, Robert "The Geometrical Foundation of Natural Structure: A Source Book of Design" New York: Dover, 1979. p38
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