Cantic octagonal tiling

Tritetratrigonal tiling

Poincaré disk model of the hyperbolic plane
TypeHyperbolic uniform tiling
Vertex figure3.6.4.6
Schläfli symbolh2{8,3}
Wythoff symbol4 3 | 3
Coxeter diagram =
Symmetry group[(4,3,3)], (*433)
DualOrder-4-3-3 t12 dual tiling
PropertiesVertex-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

Related polyhedra and tiling

Uniform (4,3,3) tilings
Symmetry: [(4,3,3)], (*433) [(4,3,3)]+, (433)
h{8,3}
t0{(4,3,3)}
{(4,3,3)}
r{8,3}
t0,1{(4,3,3)}
r{(3,4,3)}
h{8,3}
t1{(4,3,3)}
{(3,3,4)}
h2{8,3}
t1,2{(4,3,3)}
r{(4,3,3)}
{3,8}
t2{(4,3,3)}
{(3,4,3)}
h2{8,3}
t0,2{(4,3,3)}
r{(3,3,4)}
t{3,8}
t0,1,2{(4,3,3)}
t{(3,4,3)}
s{3,8}
 
s{(3,4,3)}
Uniform duals
V(3.4)3 V3.8.3.8 V(3.4)3 V3.6.4.6 V(3.3)4 V3.6.4.6 V6.6.8 V3.3.3.3.3.4
Family of cantic polyhedra and tilings: 3.6.n.6
Symmetry
*n32
[1+,2n,3]
= [(n,3,3)]
Spherical Planar Compact Hyperbolic Paracompact
*332
[1+,4,3]
Td
*333
[1+,6,3]
P3m1
*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)]
Cantic
figure

3.6.2.6

3.6.3.6

3.6.4.6

3.6.5.6

3.6.6.6

3.6..6
Coxeter
Schläfli
=
h2{4,3}
=
h2{6,3}
=
h2{8,3}
=
h2{10,3}
=
h2{12,3}
=
h2{,3}
Dual figure
V3.6.2.6

V3.6.3.6

V3.6.4.6

V3.6.5.6

V3.6.6.6

V3.6..6
Coxeter

References

See also

Wikimedia Commons has media related to Uniform tiling 3-6-4-6.

External links