Related Polyhedra and Tilings
This semiregular tiling is a member of a sequence of snubbed polyhedra and tilings with vertex figure (3.3.3.3.n) and Coxeter–Dynkin diagram . These figures and their duals have (n32) rotational symmetry, being in the Euclidean plane for n=6, and hyperbolic plane for any higher n. The series can be considered to begin with n=2, with one set of faces degenerated into digons.
| Symmetry n32 + |
Spherical | Euclidean | Hyperbolic | |||||
|---|---|---|---|---|---|---|---|---|
| 232 + D3 |
332 + T |
432 + O |
532 + I |
632 + P6 |
732 + |
832 + |
∞32 + |
|
| Snub figure |
3.3.3.3.2 |
3.3.3.3.3 |
3.3.3.3.4 |
3.3.3.3.5 |
3.3.3.3.6 |
3.3.3.3.7 |
3.3.3.3.8 |
3.3.3.3.∞ |
| Coxeter Schläfli |
s{2,3} |
s{3,3} |
s{4,3} |
s{5,3} |
s{6,3} |
s{7,3} |
s{8,3} |
s{∞,3} |
| Snub dual figure |
V3.3.3.3.2 |
V3.3.3.3.3 |
V3.3.3.3.4 |
V3.3.3.3.5 |
V3.3.3.3.6 |
V3.3.3.3.7 |
V3.3.3.3.8 | V3.3.3.3.∞ |
| Coxeter | ||||||||
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 | |||
Read more about this topic: Snub Heptagonal Tiling
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