In hyperbolic geometry, a uniform hyperbolic tiling is an edge-to-edge filling of the hyperbolic plane which has regular polygons as faces and is vertex-transitive. The tiling has a high degree of rotational and translational symmetry and all vertices are congruent.
What?
Okay so each right triangle face has three types of vertices: one with 4 triangles, one with 6 triangles, and one with 14 triangles ..and one square and one heptagon and one tetrakaidecagon at each vertex.
How did it get the name then?
The name 3-7 kisrhombille came from the 3-7 rhombic tiling, divided by a kis operator, adding a center point to each rhombus, and dividing into four triangles.
So..?
The kisrhombille tiling can be used for modeling deltahedra, as each of the equilateral triangles can serve as faces, the edges are isosceles triangles.
Conclusion: just remember 42, and maybe someday you will understand.
