The image shows a Poincaré disk model projection of the hyperbolic plane.

It is the dual tessellation of the truncated triheptagonal tiling which has one square and one heptagon and one tetrakaidecagon at each vertex.

The name 3-7 kisrhombille is given by Conway, seeing it as a 3-7 rhombic tiling, divided by a kis operator, adding a center point to each rhombus, and dividing into four triangles.

This group is special for having all even number of edges per vertex and form bisecting planes through the polyhedra and infinite lines in the plane, and are the reflection domains for the (2,3,n) triangle groups – for the heptagonal tiling, the important (2,3,7) triangle group.

The kisrhombille tilings can be seen as from the sequence of rhombille tilings, starting with the cube, with faces divided or kissed at the corners by a face central point.