View source for 4-5 kisrhombille

{{Infobox face-uniform tiling  |
  Name=4-5 kisrhombille|
  Image_File=H2-5-4-kisrhombille.svg|
  Type=[[Uniform tilings in hyperbolic plane|Dual semiregular hyperbolic tiling]]|
  Cox={{CDD|node_f1|4|node_f1|5|node_f1}} |
  Face_List=[[Triangle|Right triangle]]|
  Edge_Count=Infinite|
  Vertex_Count=Infinite|
  Symmetry_Group=[5,4], (*542)|
  Rotation_Group=[5,4]<sup>+</sup>, (542)|
  Face_Type=V4.8.10|
  Dual=[[Truncated tetrapentagonal tiling|truncated tetrapentagonal tiling]]|
  Property_List=face-transitive|
}}

In [[Geometry|geometry]], the '''4-5 kisrhombille''' or '''order-4 bisected pentagonal tiling''' is a semiregular dual [[Uniform tilings in hyperbolic plane|tiling of the hyperbolic plane]]. It is constructed by congruent [[Right triangle|right triangle]]s with 4, 8, and 10 triangles meeting at each vertex.

The name '''4-5 kisrhombille''' is by [[Biography:John Horton Conway|Conway]], seeing it as a 4-5 rhombic tiling, divided by a kis operator, adding a center point to each rhombus, and dividing into four triangles.

The image shows a [[Poincaré disk model]] projection of the hyperbolic plane.

It is labeled V4.8.10 because each right triangle face has three types of vertices: one with 4 triangles, one with 8 triangles, and one with 10 triangles.

== Dual tiling ==
It is the dual tessellation of the [[Truncated tetrapentagonal tiling|truncated tetrapentagonal tiling]] which has one square and one [[Octagon|octagon]] and one [[Decagon|decagon]] at each vertex.

[[File:H2-5-4-omnitruncated.svg|160px]]

== Related polyhedra and tilings ==

== References ==
* [[Biography:John Horton Conway|John H. Conway]], Heidi Burgiel, Chaim Goodman-Strauss, ''The Symmetries of Things'' 2008, {{ISBN|978-1-56881-220-5}} (Chapter 19, The Hyperbolic Archimedean Tessellations)

== See also ==
* Hexakis triangular tiling
* List of uniform tilings
* [[Uniform tilings in hyperbolic plane]]

{{Tessellation}}

[[Category:Hyperbolic tilings]]
[[Category:Isohedral tilings]]
[[Category:Semiregular tilings]]

eo:Ordo-3 dusekcita seplatera kahelaro

{{Sourceattribution|4-5 kisrhombille}}