| 4-5 kisrhombille | |
| Type: | Dual semiregular hyperbolic tiling |
| Face List: | Right triangle |
| Edge Count: | Infinite |
| Vertex Count: | Infinite |
| Symmetry Group: | [5,4], (*542) |
| Rotation Group: | [5,4]+, (542) |
| Face Type: | V4.8.10 |
| Dual: | truncated tetrapentagonal tiling |
| Property List: | 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.
It is the dual tessellation of the truncated tetrapentagonal tiling which has one square and one octagon and one decagon at each vertex.