Elongated triangular tiling

Elongated triangular tiling

In geometry, the elongated triangular tiling is a semiregular tiling of the Euclidean plane. There are three triangles and two squares on each vertex.

Conway calls it a isosnub quadrille.

There are 3 regular and 8 semiregular tilings in the Euclidean plane.

This tiling is related to the snub square tiling which also has 3 triangles and two squares on a vertex, but in a different order.

This is also the only uniform tiling that can't be created as a Wythoff construction. It can be constructed as alternate layers of apeirogonal prisms and apeirogonal antiprisms.

There is only one uniform coloring of an elongated triangular tiling. (Naming the colors by indices around a vertex ( 11122.) A second nonuniform coloring 11123 also exists. The coloring shown is a mixture of 12134 and 21234 colorings.

ee also

* Tilings of regular polygons


* (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. p37

External links


Wikimedia Foundation. 2010.

Look at other dictionaries:

  • Elongated triangular prismatic honeycomb — The elongated triangular prismatic honeycomb is a space filling tessellation (or honeycomb) in Euclidean 3 space. It is comprised of cubes and triangular prisms in a ratio of 1:2.It is constructed from an elongated triangular tiling extruded into …   Wikipedia

  • Prismatic pentagonal tiling — Infobox face uniform tiling Type=Dual semiregular tiling Face List=irregular pentagons Symmetry Group=cmm or 2*22 Face Type=V3. Dual=Elongated triangular tiling Property List=face transitive In geometry, the prismatic pentagonal tiling is… …   Wikipedia

  • Snub square tiling — In geometry, the snub square tiling is a semiregular tiling of the Euclidean plane. There are three triangles and two squares on each vertex. It has Schläfli symbol of s{4,4} .Conway calls it a snub quadrille, constructed as a snub operation… …   Wikipedia

  • Wythoff construction — Wythoffian constructions from 3 mirrors forming a right triangle. In geometry, a Wythoff construction, named after mathematician Willem Abraham Wythoff, is a method for constructing a uniform polyhedron or plane tiling. It is often referred to as …   Wikipedia

  • List of mathematics articles (E) — NOTOC E E₇ E (mathematical constant) E function E₈ lattice E₈ manifold E∞ operad E7½ E8 investigation tool Earley parser Early stopping Earnshaw s theorem Earth mover s distance East Journal on Approximations Eastern Arabic numerals Easton s… …   Wikipedia

  • Convex uniform honeycomb — The alternated cubic honeycomb is one of 28 space filling uniform tessellations in Euclidean 3 space, composed of alternating yellow tetrahedra and red octahedra. In geometry, a convex uniform honeycomb is a uniform tessellation which fills three …   Wikipedia

  • Teselado regular — Un teselado regular, teselación regular o teselado con polígonos regulares es una teselación o teselado del plano que emplea un solo tipo de polígonos regulares,[1] que ha sido ampliamente utilizada desde la antigüedad. Solo son posibles… …   Wikipedia Español

  • 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

  • arts, East Asian — Introduction       music and visual and performing arts of China, Korea, and Japan. The literatures of these countries are covered in the articles Chinese literature, Korean literature, and Japanese literature.       Some studies of East Asia… …   Universalium

  • 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