| Truncated order-3 apeirogonal tiling | |
|---|---|
| Poincaré disk model of the hyperbolic plane | |
| Type | Hyperbolic uniform tiling |
| Vertex configuration | 3.∞.∞ |
| Schläfli symbol | t{∞,3} |
| Wythoff symbol | 2 3 | ∞ |
| Coxeter diagram | |
| Symmetry group | [∞,3], (*∞32) |
| Dual | Infinite-order triakis triangular tiling |
| Properties | Vertex-transitive |
In geometry, the truncated order-3 apeirogonal tiling is a uniform tiling of the hyperbolic plane with a Schläfli symbol of t{∞,3}.
Related Image Collections
Add Image
We don't have any YouTube videos related to Truncated order-3 apeirogonal tiling yet.
You can add one yourself here.
We don't have any PDF documents related to Truncated order-3 apeirogonal tiling yet.
You can add one yourself here.
We don't have any Books related to Truncated order-3 apeirogonal tiling yet.
You can add one yourself here.
We don't have any archived web articles related to Truncated order-3 apeirogonal tiling yet.
Dual tiling
The dual tiling, the infinite-order triakis triangular tiling, has face configuration V3.∞.∞.
Related polyhedra and tiling
This hyperbolic tiling is topologically related as a part of sequence of uniform truncated polyhedra with vertex configurations (3.2n.2n), and [n,3] Coxeter group symmetry.
*n32 symmetry mutation of truncated tilings: t{n,3}
| |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Symmetry*n32[n,3] | Spherical | Euclid. | Compact hyperb. | Paraco. | Noncompact hyperbolic | ||||||
| *232[2,3] | *332[3,3] | *432[4,3] | *532[5,3] | *632[6,3] | *732[7,3] | *832[8,3]... | *∞32[∞,3] | [12i,3] | [9i,3] | [6i,3] | |
| Truncatedfigures | |||||||||||
| Symbol | t{2,3} | t{3,3} | t{4,3} | t{5,3} | t{6,3} | t{7,3} | t{8,3} | t{∞,3} | t{12i,3} | t{9i,3} | t{6i,3} |
| Triakisfigures | |||||||||||
| Config. | V3.4.4 | V3.6.6 | V3.8.8 | V3.10.10 | V3.12.12 | V3.14.14 | V3.16.16 | V3.∞.∞ | |||
Paracompact uniform tilings in [∞,3] family
| ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Symmetry: [∞,3], (*∞32) | [∞,3]+(∞32) | [1+,∞,3](*∞33) | [∞,3+](3*∞) | |||||||
| = | = | = | = or | = or | = | |||||
| {∞,3} | t{∞,3} | r{∞,3} | t{3,∞} | {3,∞} | rr{∞,3} | tr{∞,3} | sr{∞,3} | h{∞,3} | h2{∞,3} | s{3,∞} |
| Uniform duals | ||||||||||
| V∞3 | V3.∞.∞ | V(3.∞)2 | V6.6.∞ | V3∞ | V4.3.4.∞ | V4.6.∞ | V3.3.3.3.∞ | V(3.∞)3 | V3.3.3.3.3.∞ | |
See also
Wikimedia Commons has media related to Uniform tiling 3-i-i.- 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.