Order 3-7 kisrhombille
|Order 3-7 kisrhombille|
|Type||Dual semiregular hyperbolic tiling|
|Symmetry group||[7,3], (*732)|
|Rotation group||[7,3]+, (732)|
|Dual||Truncated triheptagonal tiling|
|Wikimedia Commons has media related to Uniform dual tiling V 4-6-14.|
The image shows a Poincaré disk model projection of the hyperbolic plane.
It is labeled V4.6.14 because each right triangle face has three types of vertices: one with 4 triangles, one with 6 triangles, and one with 14 triangles. It is the dual tessellation of the truncated triheptagonal tiling which has one square and one heptagon and one tetrakaidecagon at each vertex.
There are no mirror removal subgroups of [7,3]. The only small index subgroup is the alternation, [7,3]+, (732).
Related polyhedra and tilings
Three isohedral (regular or quasiregular) tilings can be constructed from this tiling by combining triangles:
|Heptagonal tiling||Triangular tiling||Rhombic tiling|
|Symmetry: [7,3], (*732)||[7,3]+, (732)|
It is topologically related to a polyhedra sequence; see discussion. 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.
|Spherical||Euclid.||Compact hyperb.||Paraco.||Noncompact hyperbolic|
Just as the (2,3,7) triangle group is a quotient of the modular group (2,3,∞), the associated tiling is the quotient of the modular tiling, as depicted in the video at right.
- Hexakis triangular tiling
- Tilings of regular polygons
- List of uniform tilings
- Uniform tilings in hyperbolic plane