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4 5 kisrhombille

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Faces  Right triangle
Vertices  Infinite
Rotation group  [5,4], (542)
Edges  Infinite
Symmetry group  [5,4], (*542)
4-5 kisrhombille
Type  Dual semiregular hyperbolic tiling

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 truncated tetrapentagonal tiling which has one square and one octagon and one decagon at each vertex.


4-5 kisrhombille Wikipedia

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