# Triakis triangular tiling

Triakis triangular tiling

Infobox face-uniform polyhedron

Polyhedron_Type = Dual semiregular tiling
Face_List = triangle
Edge_Count = Infinite
Vertex_Count = Infinite
Symmetry_Group = p6m
or *632
Face_Type = V3.12.12
Dual = Truncated hexagonal tiling
Property_List = face-transitive
In geometry, the Triakis triangular tiling is a tiling of the Euclidean plane. It is an equilateral triangular tiling with each triangle divided into three triangles from the center point.

It is labeled V3.12.12 because each isosceles triangle face has two types of vertices: one with 3 triangles, and two with 12 triangles. It is the dual tessellation of the truncated hexagonal tiling which has one triangle and two dodecagons at each vertex.

It is topologically related to a sequence of polyhedra and continue into tilings of the hyperbolic plane. These vertex-transitive figures have (*n32) reflectional symmetry.

* Tilings of regular polygons
* List of uniform tilings

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. p39

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