- 4-5 kisrhombille
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4-5 kisrhombille 
Type Dual semiregular hyperbolic tiling Faces Right triangle Face configuration V4.8.10 Symmetry group *542 Dual Great rhombitetrapentagonal tiling Properties face-transitive 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
It is the dual tessellation of the great rhombitetrapentagonal tiling which has one square and one octagon and one decagon at each vertex.
References
- 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
- Hexakis triangular tiling
- Tilings of regular polygons
- List of uniform tilings
- Uniform tilings in hyperbolic plane
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