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In geometry, the truncated order-3 apeirogonal tiling is a uniform tiling of the hyperbolic plane with a Schläfli symbol of t{∞,3}.
| 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 |
The dual tiling, the infinite-order triakis triangular tiling, has face configuration V3.∞.∞.
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] | |
| Truncated figures |
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| 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} |
| Triakis figures |
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| Config. | V3.4.4 | V3.6.6 | V3.8.8 | V3.10.10 | V3.12.12 | V3.14.14 | V3.16.16 | V3.∞.∞ | |||
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Wikimedia Commons has media related to Uniform tiling 3-i-i.
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