4-5 kisrhombille

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4-5 kisrhombille
Order-4 bisected pentagonal tiling.png
TypeDual semiregular hyperbolic tiling
FacesRight triangle
Coxeter diagramCDel node f1.pngCDel 4.pngCDel node f1.pngCDel 5.pngCDel node f1.png
Symmetry group[5,4], (*542)
Rotation group[5,4]+, (542)
Dual polyhedrontruncated tetrapentagonal tiling
Face configurationV4.8.10

In geometry, the 4-5 kisrhombille or order-4 bisected pentagonal tiling is a semiregular dual tiling of the hyperbolic plane. It is constructed by congruent right triangles with 4, 8, and 10 triangles meeting at each vertex.

The name 4-5 kisrhombille is by 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[edit]

It is the dual tessellation of the truncated tetrapentagonal tiling which has one square and one octagon and one decagon at each vertex.

Uniform tiling 54-t012.png


  • John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 (Chapter 19, The Hyperbolic Archimedean Tessellations)

See also[edit]