Related Polyhedra and Tilings
The triheptagonal tiling can be seen in a sequence of quasiregular polyhedrons and tilings:
| Symmetry *n32 |
Spherical | Euclidean | Hyperbolic tiling | ||||
|---|---|---|---|---|---|---|---|
| *332 Td |
*432 Oh |
*532 Ih |
*632 p6m |
*732 |
*832 |
*∞32 |
|
| Quasiregular figures configuration |
3.3.3.3 |
3.4.3.4 |
3.5.3.5 |
3.6.3.6 |
3.7.3.7 |
3.8.3.8 |
3.∞.3.∞ |
| Coxeter diagram | |||||||
| Dual (rhombic) figures configuration |
V3.3.3.3 |
V3.4.3.4 |
V3.5.3.5 |
V3.6.3.6 |
V3.7.3.7 |
V3.8.3.8 |
V3.∞.3.∞ |
| Coxeter diagram | |||||||
From a Wythoff construction there are eight hyperbolic uniform tilings that can be based from the regular heptagonal tiling.
Drawing the tiles colored as red on the original faces, yellow at the original vertices, and blue along the original edges, there are 8 forms.
| Symmetry:, (*732) | +, (732) | |||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| {7,3} | t0,1{7,3} | t1{7,3} | t1,2{7,3} | t2{7,3} | t0,2{7,3} | t0,1,2{7,3} | s{7,3} | |||
| Uniform duals | ||||||||||
| V73 | V3.14.14 | V3.7.3.7 | V6.6.7 | V37 | V3.4.7.4 | V4.6.14 | V3.3.3.3.7 | |||
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