Snub tetrahexagonal tiling
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| Snub tetrahexagonal tiling | |
|---|---|
| Snub tetrahexagonal tiling Poincaré disk model of the hyperbolic plane | |
| Type | Hyperbolic uniform tiling |
| Vertex configuration | 3.3.4.3.6 |
| Schläfli symbol | sr{6,4} or |
| Wythoff symbol | | 6 4 2 |
| Coxeter diagram | File:CDel node h.pngFile:CDel 6.pngFile:CDel node h.pngFile:CDel 4.pngFile:CDel node h.png or File:CDel node h.pngFile:CDel split1-64.pngFile:CDel nodes hh.png |
| Symmetry group | [6,4]+, (642) |
| Dual | Order-6-4 floret pentagonal tiling |
| Properties | Vertex-transitive Chiral |
In geometry, the snub tetrahexagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of sr{6,4}.
Images
Drawn in chiral pairs, with edges missing between black triangles:
Related polyhedra and tiling
The snub tetrahexagonal tiling is fifth in a series of snub polyhedra and tilings with vertex figure 3.3.4.3.n.
| 4n2 symmetry mutations of snub tilings: 3.3.4.3.n | ||||||||
|---|---|---|---|---|---|---|---|---|
| Symmetry 4n2 |
Spherical | Euclidean | Compact hyperbolic | Paracomp. | ||||
| 242 | 342 | 442 | 542 | 642 | 742 | 842 | ∞42 | |
| Snub figures |
File:Spherical square antiprism.svg | File:Spherical snub cube.png | File:Uniform tiling 44-snub.png | File:H2-5-4-snub.svg | File:Uniform tiling 64-snub.png | File:Uniform tiling 74-snub.png | File:Uniform tiling 84-snub.png | File:Uniform tiling i42-snub.png |
| Config. | 3.3.4.3.2 | 3.3.4.3.3 | 3.3.4.3.4 | 3.3.4.3.5 | 3.3.4.3.6 | 3.3.4.3.7 | 3.3.4.3.8 | 3.3.4.3.∞ |
| Gyro figures |
File:Spherical tetragonal trapezohedron.svg | File:Spherical pentagonal icositetrahedron.svg | File:Tiling Dual Semiregular V3-3-4-3-4 Cairo Pentagonal.svg | File:H2-5-4-floret.svg | ||||
| Config. | V3.3.4.3.2 | V3.3.4.3.3 | V3.3.4.3.4 | V3.3.4.3.5 | V3.3.4.3.6 | V3.3.4.3.7 | V3.3.4.3.8 | V3.3.4.3.∞ |
References
- John H. Conway, Heidi Burgiel, Chaim Goodman-Strauss, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 (Chapter 19, The Hyperbolic Archimedean Tessellations)
- "Chapter 10: Regular honeycombs in hyperbolic space". The Beauty of Geometry: Twelve Essays. Dover Publications. 1999. ISBN 0-486-40919-8. LCCN 99035678.
See also
Wikimedia Commons has media related to Uniform tiling 3-3-4-3-6.
