Related Polyhedra and Tilings
It is topologically related to a polyhedra sequence defined by the face configuration V4.6.2n. 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 continuing into the hyperbolic plane for any
With an even number of faces at every vertex, these polyhedra and tilings can be shown by alternating two colors so all adjacent faces have different colors.
Each face on these domains also corresponds to the fundamental domain of a symmetry group with order 2,3,n mirrors at each triangle face vertex.
| n | 2 | 3 | 4 | 5 |
|---|---|---|---|---|
| Tiling space | Spherical | |||
| Face configuration V4.6.2n |
V4.6.4 | V4.6.6 | V4.6.8 | V4.6.10 |
| Symmetry group (Orbifold) |
D3h, (*322) D6h (*622) full sym. |
Td (*332) Oh (*432) full sym. |
Oh (*432) | Ih (*532) |
| Symmetry fundamental domain |
(Order 12) |
(Order 24) |
(Order 48) |
(Order 60) |
| Polyhedron | ||||
| Coxeter diagram | ||||
| Net | ||||
| n | 6 | 7 | 8 | ...∞ |
|---|---|---|---|---|
| Tiling space | Euclidean | Hyperbolic | ||
| Face configuration V4.6.2n |
V4.6.12 | V4.6.14 | V4.6.16 | ...V4.6.∞ |
| Symmetry group (orbifold notation) |
(*632) | (*732) | (*832) | ...(*∞32) |
| Tiling | ... | |||
| Coxeter diagram | ... | |||
The kisrhombille tiling is a part of a set of uniform dual tilings, corresponding to the dual of the truncated trihexagonal tiling.
| Wythoff | 3 | 6 2 | 2 3 | 6 | 2 | 6 3 | 2 6 | 3 | 6 | 3 2 | 6 3 | 2 | 6 3 2 | | | 6 3 2 | |||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Schläfli | {6,3} | t0,1{6,3} | t1{6,3} | t1,2{6,3} | t2{6,3} | t0,2{6,3} | t0,1,2{6,3} | s{6,3} | h0{6,3} | h1,2{6,3} | |
| Coxeter | |||||||||||
| Image Vertex figure |
6.6.6 |
3.12.12 |
3.6.3.6 |
6.6.6 |
{36} |
3.4.6.4 |
4.6.12 |
3.3.3.3.6 |
(3.3)3 |
3.3.3.3.3.3 |
|
| Uniform duals | |||||||||||
| Coxeter | |||||||||||
| Image Vertex figure |
V6.6.6 |
V3.12.12 |
V3.6.3.6 |
V6.6.6 |
V3.3.3.3.3.3 |
V3.4.6.4 |
V4.6.12 |
V3.3.3.3.6 |
V(3.3)3 |
||
Read more about this topic: Bisected Hexagonal Tiling
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