Truncated infinite-order triangular tiling

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Infinite-order truncated triangular tiling
Truncated infinite-order triangular tiling
Poincaré disk model of the hyperbolic plane
Type Hyperbolic uniform tiling
Vertex figure ∞.6.6
Schläfli symbol t{3,∞}
Wythoff symbol 2 ∞ | 3
Coxeter diagram CDel node.pngCDel infin.pngCDel node 1.pngCDel 3.pngCDel node 1.png
Symmetry group [∞,3], (*∞32)
Dual apeirokis apeirogonal tiling
Properties Vertex-transitive

In geometry, the truncated infinite-order triangular tiling is a uniform tiling of the hyperbolic plane with a Schläfli symbol of t{3,∞}.

Dual tiling[edit]

H2checkers 33i.png

Related polyhedra and tiling[edit]

This hyperbolic tiling is topologically related as a part of sequence of uniform truncated polyhedra with vertex configurations (6.n.n), and [n,3] Coxeter group symmetry.

Dimensional family of truncated polyhedra and tilings: n.6.6
Symmetry
*n42
[n,3]
Spherical Euclidean Compact hyperbolic Paracompact
*232
[2,3]
D3h
*332
[3,3]
Td
*432
[4,3]
Oh
*532
[5,3]
Ih
*632
[6,3]
P6m
*732
[7,3]
 
*832
[8,3]...
 
*∞32
[∞,3]
 
Order 12 24 48 120
Truncated
figures
Hexagonal dihedron.png
2.6.6
Uniform tiling 332-t12.png
3.6.6
Uniform tiling 432-t12.png
4.6.6
Uniform tiling 532-t12.png
5.6.6
Uniform tiling 63-t12.png
6.6.6
Uniform tiling 73-t12.png
7.6.6
Uniform tiling 83-t12.png
8.6.6
H2 tiling 23i-6.png
∞.6.6
Coxeter
Schläfli
CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 2.pngCDel node.png
t{3,2}
CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 3.pngCDel node.png
t{3,3}
CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 4.pngCDel node.png
t{3,4}
CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 5.pngCDel node.png
t{3,5}
CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 6.pngCDel node.png
t{3,6}
CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 7.pngCDel node.png
t{3,7}
CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 8.pngCDel node.png
t{3,8}
CDel node 1.pngCDel 3.pngCDel node 1.pngCDel infin.pngCDel node.png
t{3,∞}
Uniform dual figures
n-kis
figures
Hexagonal Hosohedron.svg
V2.6.6
Triakistetrahedron.jpg
V3.6.6
Tetrakishexahedron.jpg
V4.6.6
Pentakisdodecahedron.jpg
V5.6.6
Uniform tiling 63-t2.png
V6.6.6
Order3 heptakis heptagonal til.png
V7.6.6
Uniform dual tiling 433-t012.png
V8.6.6
H2checkers 33i.png
V∞.6.6
Coxeter CDel node f1.pngCDel 3.pngCDel node f1.pngCDel 2.pngCDel node.png CDel node f1.pngCDel 3.pngCDel node f1.pngCDel 3.pngCDel node.png CDel node f1.pngCDel 3.pngCDel node f1.pngCDel 4.pngCDel node.png CDel node f1.pngCDel 3.pngCDel node f1.pngCDel 5.pngCDel node.png CDel node f1.pngCDel 3.pngCDel node f1.pngCDel 6.pngCDel node.png CDel node f1.pngCDel 3.pngCDel node f1.pngCDel 7.pngCDel node.png CDel node f1.pngCDel 3.pngCDel node f1.pngCDel 8.pngCDel node.png CDel node f1.pngCDel 3.pngCDel node f1.pngCDel infin.pngCDel node.png
Noncompact hyperbolic uniform tilings in [∞,3] family
Symmetry: [∞,3], (*∞32) [∞,3]+
(∞32)
[1+,∞,3]
(*∞33)
[∞,3+]
(3*∞)
CDel node 1.pngCDel infin.pngCDel node.pngCDel 3.pngCDel node.png CDel node 1.pngCDel infin.pngCDel node 1.pngCDel 3.pngCDel node.png CDel node.pngCDel infin.pngCDel node 1.pngCDel 3.pngCDel node.png CDel node.pngCDel infin.pngCDel node 1.pngCDel 3.pngCDel node 1.png CDel node.pngCDel infin.pngCDel node.pngCDel 3.pngCDel node 1.png CDel node 1.pngCDel infin.pngCDel node.pngCDel 3.pngCDel node 1.png CDel node 1.pngCDel infin.pngCDel node 1.pngCDel 3.pngCDel node 1.png CDel node h.pngCDel infin.pngCDel node h.pngCDel 3.pngCDel node h.png CDel node h1.pngCDel infin.pngCDel node.pngCDel 3.pngCDel node.png CDel node h1.pngCDel infin.pngCDel node.pngCDel 3.pngCDel node 1.png CDel node.pngCDel infin.pngCDel node h.pngCDel 3.pngCDel node h.png
CDel node h0.pngCDel infin.pngCDel node 1.pngCDel 3.pngCDel node.png
= CDel labelinfin.pngCDel branch 11.pngCDel split2.pngCDel node.png
CDel node h0.pngCDel infin.pngCDel node 1.pngCDel 3.pngCDel node 1.png
= CDel labelinfin.pngCDel branch 11.pngCDel split2.pngCDel node 1.png
CDel node h0.pngCDel infin.pngCDel node.pngCDel 3.pngCDel node 1.png
= CDel labelinfin.pngCDel branch.pngCDel split2.pngCDel node 1.png
CDel node 1.pngCDel infin.pngCDel node h.pngCDel 3.pngCDel node h.png CDel node h1.pngCDel infin.pngCDel node.pngCDel 3.pngCDel node.png =
CDel labelinfin.pngCDel branch 10ru.pngCDel split2.pngCDel node.png or CDel labelinfin.pngCDel branch 01rd.pngCDel split2.pngCDel node.png
CDel node h1.pngCDel infin.pngCDel node.pngCDel 3.pngCDel node 1.png =
CDel labelinfin.pngCDel branch 10ru.pngCDel split2.pngCDel node 1.png or CDel labelinfin.pngCDel branch 01rd.pngCDel split2.pngCDel node 1.png
CDel node h0.pngCDel infin.pngCDel node h.pngCDel 3.pngCDel node h.png
= CDel labelinfin.pngCDel branch hh.pngCDel split2.pngCDel node h.png
H2 tiling 23i-1.png H2 tiling 23i-3.png H2 tiling 23i-2.png H2 tiling 23i-6.png H2 tiling 23i-4.png H2 tiling 23i-5.png H2 tiling 23i-7.png Uniform tiling i32-snub.png H2 tiling 33i-1.png
{∞,3} t{∞,3} r{∞,3} t{3,∞} {3,∞} rr{∞,3} tr{∞,3} sr{∞,3} h{∞,3} h2{∞,3} s{3,∞}
Uniform duals
CDel node f1.pngCDel infin.pngCDel node.pngCDel 3.pngCDel node.png CDel node f1.pngCDel infin.pngCDel node f1.pngCDel 3.pngCDel node.png CDel node.pngCDel infin.pngCDel node f1.pngCDel 3.pngCDel node.png CDel node.pngCDel infin.pngCDel node f1.pngCDel 3.pngCDel node f1.png CDel node.pngCDel infin.pngCDel node.pngCDel 3.pngCDel node f1.png CDel node f1.pngCDel infin.pngCDel node.pngCDel 3.pngCDel node f1.png CDel node f1.pngCDel infin.pngCDel node f1.pngCDel 3.pngCDel node f1.png CDel node fh.pngCDel infin.pngCDel node fh.pngCDel 3.pngCDel node fh.png CDel node fh.pngCDel infin.pngCDel node.pngCDel 3.pngCDel node.png CDel node.pngCDel infin.pngCDel node fh.pngCDel 3.pngCDel node fh.png
H2 tiling 23i-4.png Ord-infin triakis triang til.png Ord3infin qreg rhombic til.png H2checkers 33i.png H2 tiling 23i-1.png Deltoidal triapeirogonal til.png H2checkers 23i.png Order-3-infinite floret pentagonal tiling.png Alternate order-3 apeirogonal tiling.png
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[edit]

References[edit]

External links[edit]