# 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.

** See also **

* 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

*Wikimedia Foundation.
2010.*

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