Cantic octagonal tiling

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Tritetratrigonal tiling
Cantic octagonal tiling
Poincaré disk model of the hyperbolic plane
Type Hyperbolic uniform tiling
Vertex configuration 3.6.4.6
Schläfli symbol h2{8,3}
Wythoff symbol 4 3 | 3
Coxeter diagram CDel label4.pngCDel branch 10ru.pngCDel split2.pngCDel node 1.png = CDel node h1.pngCDel 8.pngCDel node.pngCDel 3.pngCDel node 1.png
Symmetry group [(4,3,3)], (*433)
Dual Order-4-3-3 t12 dual tiling
Properties Vertex-transitive

In geometry, the tritetratrigonal tiling or shieldotritetragonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t1,2(4,3,3). It can also be named as a cantic octagonal tiling, h2{8,3}.

Dual tiling

240px

Related polyhedra and tiling

*n33 orbifold symmetries of cantic tilings: 3.6.n.6
Symmetry
*n32
[1+,2n,3]
= [(n,3,3)]
Spherical Euclidean Compact Hyperbolic Paracompact
*233
[1+,4,3]
= [3,3]
*333
[1+,6,3]
= [(3,3,3)]
*433
[1+,8,3]
= [(4,3,3)]
*533
[1+,10,3]
= [(5,3,3)]
*633...
[1+,12,3]
= [(6,3,3)]
*∞33
[1+,∞,3]
= [(∞,3,3)]
Coxeter
Schläfli
CDel node h1.pngCDel 4.pngCDel node.pngCDel 3.pngCDel node 1.png = CDel nodes 10ru.pngCDel split2.pngCDel node 1.png
h2{4,3}
CDel node h1.pngCDel 6.pngCDel node.pngCDel 3.pngCDel node 1.png = CDel branch 10ru.pngCDel split2.pngCDel node 1.png
h2{6,3}
CDel node h1.pngCDel 8.pngCDel node.pngCDel 3.pngCDel node 1.png = CDel label4.pngCDel branch 10ru.pngCDel split2.pngCDel node 1.png
h2{8,3}
CDel node h1.pngCDel 10.pngCDel node.pngCDel 3.pngCDel node 1.png = CDel label5.pngCDel branch 10ru.pngCDel split2.pngCDel node 1.png
h2{10,3}
CDel node h1.pngCDel 12.pngCDel node.pngCDel 3.pngCDel node 1.png = CDel label6.pngCDel branch 10ru.pngCDel split2.pngCDel node 1.png
h2{12,3}
CDel node h1.pngCDel infin.pngCDel node.pngCDel 3.pngCDel node 1.png = CDel labelinfin.pngCDel branch 10ru.pngCDel split2.pngCDel node 1.png
h2{∞,3}
Cantic
figure
Spherical cantic cube.png Uniform tiling 333-t12.png H2 tiling 334-6.png H2 tiling 335-6.png H2 tiling 336-6.png H2 tiling 33i-6.png
Vertex 3.6.2.6 3.6.3.6 3.6.4.6 3.6.5.6 3.6.6.6 3.6..6
N33 fundamental domain t01.png
Domain
80px 333 fundamental domain t01.png 80px 80px 80px 80px
Wythoff 2 3 | 3 3 3 | 3 4 3 | 3 5 3 | 3 6 3 | 3 ∞ 3 | 3
Dual
figure
Spherical triakis tetrahedron.png 80px 80px
Face V3.6.2.6 V3.6.3.6 V3.6.4.6 V3.6.5.6 V3.6.6.6 V3.6.∞.6

References

  • John H. Conway, Heidi Burgiel, Chaim Goodman-Strass, The Symmetries of Things 2008, ISBN 978-1-56881-220-5 (Chapter 19, The Hyperbolic Archimedean Tessellations)
  • Lua error in package.lua at line 80: module 'strict' not found.

See also

External links

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