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.
Look at other dictionaries:
Triakis icosahedron — A triakis icosahedron is an Archimedean dual solid, or a Catalan solid. Its dual is the truncated dodecahedron.It can be seen as an icosahedron with triangular pyramids augmented to each face. This interpretation is expressed in the name.This… … Wikipedia
Order-3 truncated heptagonal tiling — Poincaré disk model Type Hyperbolic semiregular tiling Vertex figure 3.14.14 Schläfli symbol t{7 … Wikipedia
List of mathematics articles (T) — NOTOC T T duality T group T group (mathematics) T integration T norm T norm fuzzy logics T schema T square (fractal) T symmetry T table T theory T.C. Mits T1 space Table of bases Table of Clebsch Gordan coefficients Table of divisors Table of Lie … Wikipedia
Conway polyhedron notation — This example chart shows how 11 new forms can be derived from the cube using 3 operations. The new polyhedra are shown as maps on the surface of the cube so the topological changes are more apparent. Vertices are marked in all forms with circles … Wikipedia
Octahedron — For the album by The Mars Volta, see Octahedron (album). Regular Octahedron (Click here for rotating model) Type Platonic solid Elements F = 8, E = 12 V = 6 (χ = 2) Faces by sides … Wikipedia
Tetrahedron — For the academic journal, see Tetrahedron (journal). Regular Tetrahedron (Click here for rotating model) Type Platonic solid Elements F = 4, E = 6 V = 4 (χ = 2) Faces by s … Wikipedia
Cuboctahedron — (Click here for rotating model) Type Archimedean solid Uniform polyhedron Elements F = 14, E = 24, V = 12 (χ = 2) Faces by sides 8{3}+6{4} … Wikipedia
Cube — This article is about the geometric shape. For other uses, see Cube (disambiguation). Regular Hexahedron (Click here for rotating model) Type Platonic solid Elements F = 6, E = 12 V = 8 (χ = 2) … Wikipedia
Snub cube — (Click here for rotating model) Type Archimedean solid Uniform polyhedron Elements F = 38, E = 60, V = 24 (χ = 2) Faces by sides (8+24){3}+6{4} … Wikipedia
Dodecahedron — Regular Dodecahedron (Click here for rotating model) Type Platonic solid Elements F = 12, E = 30 V = 20 (χ = 2) Faces by sides 12{5} … Wikipedia
