Truncated order-7 square tiling

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Truncated order-7 square tiling
H2 tiling 247-6.png
Poincaré disk model of the hyperbolic plane
Type Hyperbolic uniform tiling
Vertex configuration 8.8.7
Schläfli symbol t{4,7}
Wythoff symbol 4
Coxeter diagram CDel node.pngCDel 7.pngCDel node 1.pngCDel 4.pngCDel node 1.png
Symmetry group [7,4], (*742)
Dual Order-4 heptakis heptagonal tiling
Properties Vertex-transitive

In geometry, the truncated order-7 square tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t0,1{4,7}.

Contents

*n42 symmetry mutation of truncated tilings: n.8.8
Symmetry
*n42
[n,4]
Spherical Euclidean Compact hyperbolicParacompact
*242
[2,4]
*342
[3,4]
*442
[4,4]
*542
[5,4]
*642
[6,4]
*742
[7,4]
*842
[8,4]...
*42
[,4]
Truncated
figures
Octagonal dihedron.svg Uniform tiling 432-t01.png Uniform tiling 44-t12.svg H2-5-4-trunc-primal.svg H2 tiling 246-6.png H2 tiling 247-6.png H2 tiling 248-6.png H2 tiling 24i-6.png
Config. 2.8.8 3.8.8 4.8.8 5.8.8 6.8.8 7.8.8 8.8.8 .8.8
n-kis
figures
Spherical octagonal hosohedron.png Spherical triakis octahedron.png 1-uniform 2 dual.svg H2-5-4-kis-dual.svg Order4 hexakis hexagonal til.png Order4 heptakis heptagonal til.png H2-8-3-primal.svg Ord4 apeirokis apeirogonal til.png
Config. V2.8.8 V3.8.8 V4.8.8 V5.8.8V6.8.8V7.8.8V8.8.8V.8.8
Uniform heptagonal/square tilings
Symmetry: [7,4], (*742) [7,4]+, (742)[7+,4], (7*2)[7,4,1+], (*772)
CDel node 1.pngCDel 7.pngCDel node.pngCDel 4.pngCDel node.pngCDel node 1.pngCDel 7.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel node.pngCDel 7.pngCDel node 1.pngCDel 4.pngCDel node.pngCDel node.pngCDel 7.pngCDel node 1.pngCDel 4.pngCDel node 1.pngCDel node.pngCDel 7.pngCDel node.pngCDel 4.pngCDel node 1.pngCDel node 1.pngCDel 7.pngCDel node.pngCDel 4.pngCDel node 1.pngCDel node 1.pngCDel 7.pngCDel node 1.pngCDel 4.pngCDel node 1.pngCDel node h.pngCDel 7.pngCDel node h.pngCDel 4.pngCDel node h.pngCDel node h.pngCDel 7.pngCDel node h.pngCDel 4.pngCDel node.pngCDel node.pngCDel 7.pngCDel node.pngCDel 4.pngCDel node h.png
Uniform tiling 74-t0.png Uniform tiling 74-t01.png Uniform tiling 74-t1.png Uniform tiling 74-t12.png Uniform tiling 74-t2.png Uniform tiling 74-t02.png Uniform tiling 74-t012.png Uniform tiling 74-snub.png Uniform tiling 74-h01.png Uniform tiling 77-t0.png
{7,4} t{7,4} r{7,4} 2t{7,4}=t{4,7} 2r{7,4}={4,7} rr{7,4} tr{7,4} sr{7,4} s{7,4} h{4,7}
Uniform duals
CDel node f1.pngCDel 7.pngCDel node.pngCDel 4.pngCDel node.pngCDel node f1.pngCDel 7.pngCDel node f1.pngCDel 4.pngCDel node.pngCDel node.pngCDel 7.pngCDel node f1.pngCDel 4.pngCDel node.pngCDel node.pngCDel 7.pngCDel node f1.pngCDel 4.pngCDel node f1.pngCDel node.pngCDel 7.pngCDel node.pngCDel 4.pngCDel node f1.pngCDel node f1.pngCDel 7.pngCDel node.pngCDel 4.pngCDel node f1.pngCDel node f1.pngCDel 7.pngCDel node f1.pngCDel 4.pngCDel node f1.pngCDel node fh.pngCDel 7.pngCDel node fh.pngCDel 4.pngCDel node fh.pngCDel node fh.pngCDel 7.pngCDel node fh.pngCDel 4.pngCDel node.pngCDel node.pngCDel 7.pngCDel node.pngCDel 4.pngCDel node fh.png
Uniform tiling 74-t2.png Hyperbolic domains 772.png Ord74 qreg rhombic til.png Order4 heptakis heptagonal til.png Uniform tiling 74-t0.png Deltoidal tetraheptagonal til.png Hyperbolic domains 742.png Uniform tiling 77-t2.png
V74V4.14.14V4.7.4.7V7.8.8V47V4.4.7.4V4.8.14V3.3.4.3.7V3.3.7.3.7V77

Related Research Articles

Triheptagonal tiling

In geometry, the triheptagonal tiling is a semiregular tiling of the hyperbolic plane, representing a rectified Order-3 heptagonal tiling. There are two triangles and two heptagons alternating on each vertex. It has Schläfli symbol of r{7,3}.

Rhombitetrapentagonal tiling

In geometry, the rhombitetrapentagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t0,2{4,5}.

Truncated order-4 pentagonal tiling

In geometry, the truncated order-4 pentagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t0,1{5,4}.

Truncated order-5 square tiling

In geometry, the truncated order-5 square tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t0,1{4,5}.

Truncated order-5 pentagonal tiling

In geometry, the truncated order-5 pentagonal tiling is a regular tiling of the hyperbolic plane. It has Schläfli symbol of t0,1{5,5}, constructed from one pentagons and two decagons around every vertex.

Truncated order-4 heptagonal tiling

In geometry, the truncated order-4 heptagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t{7,4}.

Tetraheptagonal tiling

In geometry, the tetraheptagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of r{4,7}.

Order-7 square tiling

In geometry, the order-7 square tiling is a regular tiling of the hyperbolic plane. It has Schläfli symbol of {4,7}.

Rhombitetraheptagonal tiling

In geometry, the rhombitetraheptagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of rr{4,7}. It can be seen as constructed as a rectified tetraheptagonal tiling, r{7,4}, as well as an expanded order-4 heptagonal tiling or expanded order-7 square tiling.

Truncated tetraheptagonal tiling

In geometry, the truncated tetraheptagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of tr{4,7}.

Snub tetraheptagonal tiling

In geometry, the snub tetraheptagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of sr{7,4}.

Order-7 heptagonal tiling

In geometry, the order-7 heptagonal tiling is a regular tiling of the hyperbolic plane. It has Schläfli symbol of {7,7}, constructed from seven heptagons around every vertex. As such, it is self-dual.

Truncated order-7 heptagonal tiling

In geometry, the truncated order-7 heptagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t0,1{7,7}, constructed from one heptagons and two tetrakaidecagons around every vertex.

Snub heptaheptagonal tiling

In geometry, the snub heptaheptagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of sr{7,7}, constructed from two regular heptagons and three equilateral triangles around every vertex.

Cantic octagonal tiling

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}.

Alternated order-4 hexagonal tiling

In geometry, the alternated order-4 hexagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of (3,4,4), h{6,4}, and hr{6,6}.

Truncated order-5 hexagonal tiling

In geometry, the truncated order-5 hexagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t0,1{6,5}.

Pentahexagonal tiling

In geometry, the pentahexagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of r{6,5} or t1{6,5}.

Truncated order-6 pentagonal tiling

In geometry, the truncated order-6 pentagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t1,2{6,5}.

Rhombipentahexagonal tiling

In geometry, the rhombipentahexagonal tiling is a uniform tiling of the hyperbolic plane. It has Schläfli symbol of t0,2{6,5}.

References

See also