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List of tessellations

This is a list of tessellations.

Spherical

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Regular Spherical (n=1, 2, 3, ...)
Article Vertex configuration Schläfli symbol Image
Dihedron n2 {n,2}   {6,2}
Hosohedron 2n {2,n}   {2,6}
Spherical tetrahedron 33 {3,3}  
Spherical octahedron 34 {3,4}  
Spherical cube 43 {4,3}  
Spherical icosahedron 35 {3,5}  
Spherical dodecahedron 53 {5,3}  
Semi-regular Spherical (n=2, 3, ...)
Article Vertex configuration Schläfli symbol Image
Prism 4.4.n t{2, n}
= { }×{n} 		  { }×{6}
Antiprism 33.n sr{2,n}
= { }⊗{n} 		  { }⊗{6}
Dual semi-regular Spherical (n=2, 3, ...)
Article Vertex configuration Schläfli symbol Image
Bipyramid V42.n dt{2, n}
= { }+{n} 		  { }+{6}
Trapezohedron V33.n dsr{2,n}
= { }⨁{n} 		  { }⨁{6}

Planar

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Regular
Article Vertex configuration Schläfli symbol Image
Apeirogonal hosohedron 2∞ {2,∞}  
Order-2 apeirogonal tiling ∞2 {∞,2}  
Square tiling 44 {4,4}  
Triangular tiling 36 {3,6}  
Hexagonal tiling 63 {6,3}  
Semi-regular
Article Vertex configuration Schläfli symbol Image
Apeirogonal prism 42.∞ t{2,∞}  
Apeirogonal antiprism 33.∞ sr{2,∞}  
Snub square tiling 32.4.3.4 s{4,4}  
Elongated triangular tiling 33.42 {3,6}:e  
Snub trihexagonal tiling 34.6 sr{6,3}  
Rhombitrihexagonal tiling 3.4.6.4 rr{6,3}  
Trihexagonal tiling 3.6.3.6 r{6,3}  
Truncated hexagonal tiling 3.122 t{6,3}  
Truncated trihexagonal tiling 4.6.12 tr{6,3}  
Truncated square tiling 4.82 tr{4,4}  
Dual semi-regular
Article Face configuration Schläfli symbol Image
Apeirogonal deltohedron V33.∞ dsr{2,∞}  
Apeirogonal bipyramid V42.∞ dt{2,∞}  
Cairo pentagonal tiling V32.4.3.4 ds{4,4}  
Prismatic pentagonal tiling V33.42 d{3,6}:e  
Floret pentagonal tiling V34.6 dsr{6,3}  
Deltoidal trihexagonal tiling V3.4.6.4 drr{6,3}  
Rhombille tiling V3.6.3.6 dr{6,3}  
Triakis triangular tiling V3.122 dt{6,3}  
Kisrhombille tiling V4.6.12 dtr{6,3}  
Tetrakis square tiling 4.82 tr{4,4}  

Hyperbolic

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Hyperbolic
Article Vertex configuration Schläfli symbol Image
Snub tetrapentagonal tiling 32.4.3.5 sr{5,4}  
Snub tetrahexagonal tiling 32.4.3.6 sr{6,4}  
Snub tetraheptagonal tiling 32.4.3.7 sr{7,4}  
Snub tetraoctagonal tiling 32.4.3.8 sr{8,4}  
Snub tetraapeirogonal tiling 32.4.3.∞ sr{∞,4}  
Snub pentapentagonal tiling 32.5.3.5 s{5,4}  
Snub pentahexagonal tiling 32.5.3.6 sr{6,5}  
Snub hexahexagonal tiling 32.6.3.6 s{6,4}  
Snub hexaoctagonal tiling 32.6.3.8 sr{8,6}  
Snub heptaheptagonal tiling 32.7.3.7 sr{7,7}  
Snub octaoctagonal tiling 32.8.3.8 s{8,4}  
Snub order-6 square tiling 33.4.3.4 s{4,6}  
Snub apeiroapeirogonal tiling 32.∞.3.∞ sr{∞,∞}  
Snub triheptagonal tiling 34.7 sr{7,3}  
Snub trioctagonal tiling 34.8 sr{8,3}  
Snub triapeirogonal tiling 34.∞ sr{∞,3}  
Snub order-8 triangular tiling 35.4 s{3,8}  
Order-7 triangular tiling 37 {3,7}  
Order-8 triangular tiling 38 {3,8}  
Infinite-order triangular tiling 3∞ {3,∞}
Alternated octagonal tiling 3.4.3.4.3.4 h{8,3}
Alternated order-4 hexagonal tiling 3.4.3.4.3.4.3.4 h{6,4}
Quarter order-6 square tiling 3.4.62.4 q{4,6}
Rhombitriheptagonal tiling 3.4.7.4 rr{7,3}  
Rhombitrioctagonal tiling 3.4.8.4 rr{8,3}  
Rhombitriapeirogonal tiling 3.4.∞.4 rr{∞,3}
Cantic octagonal tiling 3.6.4.6 h2{8,3}
Triheptagonal tiling 3.7.3.7 r{7,3}  
Trioctagonal tiling 3.8.3.8 r{8,3}  
Truncated heptagonal tiling 3.142 t{7,3}  
Truncated octagonal tiling 3.162 t{8,3}  
Triapeirogonal tiling 3.∞.3.∞ r{∞,3}  
Truncated order-3 apeirogonal tiling 3.∞2 t{∞,3}  
Rhombitetrapentagonal tiling 42.5.4 rr{5,4}  
Rhombitetrahexagonal tiling 42.6.4 rr{6,4}
Rhombitetraheptagonal tiling 42.7.4 rr{7,4}
Rhombitetraoctagonal tiling 42.8.4 rr{8,4}
Rhombitetraapeirogonal tiling 42.∞.4 rr{∞,4}
Order-5 square tiling 45 {4,5}  
Order-6 square tiling 46 {4,6}  
Order-7 square tiling 47 {4,7}
Order-8 square tiling 48 {4,8}
Infinite-order square tiling 4∞ {4,∞}
Tetrapentagonal tiling 4.5.4.5 r{5,4}  
Tetrahexagonal tiling 4.6.4.6 r{6,4}
Truncated trihexagonal tiling 4.6.12 tr{6,3}
Truncated triheptagonal tiling 4.6.14 tr{7,3}  
Order 3-7 kisrhombille V4.6.14 ???  
Truncated trioctagonal tiling 4.6.16 tr{8,3}  
Order 3-8 kisrhombille V4.6.16 ???  
Truncated triapeirogonal tiling 4.6.∞ tr{∞,3}
Tetraheptagonal tiling 4.7.4.7 r{7,4}
Tetraoctagonal tiling 4.8.4.8 r{8,4}
Truncated tetrapentagonal tiling 4.8.10 tr{5,4}  
4-5 kisrhombille V4.8.10 ???  
Truncated tetrahexagonal tiling 4.8.12 tr{6,4}
Truncated tetraheptagonal tiling 4.8.14 tr{7,4}
Truncated tetraoctagonal tiling 4.8.16 tr{8,4}
Truncated tetraapeirogonal tiling 4.8.∞ tr{∞,4}
Truncated order-4 pentagonal tiling 4.102 t{5,4}  
Truncated pentahexagonal tiling 4.10.12 tr{6,5}
Truncated order-4 hexagonal tiling 4.122 t{6,4}
Truncated hexaoctagonal tiling 4.12.16 tr{8,6}
Truncated order-4 heptagonal tiling 4.142 t{7,4}
Truncated order-4 octagonal tiling 4.162 t{8,4}
Truncated order-4 apeirogonal tiling 4.∞2 t{∞,4}
Tetraapeirogonal tiling 4.∞.4.∞ r{∞,4}
Order-4 pentagonal tiling 54 {5,4}  
Order-5 pentagonal tiling 55 {5,5}
Order-6 pentagonal tiling 56 {5,6}
Infinite-order pentagonal tiling 5∞ {5,∞}
Rhombipentahexagonal tiling 5.4.6.4 rr{6,5}
Pentahexagonal tiling 5.6.5.6 r{6,5}
Truncated order-5 square tiling 5.82 t{4,5}  
Truncated order-5 pentagonal tiling 5.102 t{5,5}
Truncated order-5 hexagonal tiling 5.122 t{6,5}
Pentaapeirogonal tiling 5.∞.5.∞ r{∞,5}
Order-4 hexagonal tiling 64 {6,4}
Order-5 hexagonal tiling 65 {6,5}
Order-6 hexagonal tiling 66 {6,6}
Order-8 hexagonal tiling 68 {6,8}
Rhombihexaoctagonal tiling 6.4.8.4 rr{8,6}
Hexaoctagonal tiling 6.8.6.8 r{8,6}
Truncated order-6 square tiling 6.82 t{4,6}
Truncated order-6 pentagonal tiling 6.102 t{5,6}
Truncated order-6 hexagonal tiling 6.122 t{6,6}
Truncated order-6 octagonal tiling 6.162 t{8,6}
Heptagonal tiling 73 {7,3}  
Order-4 heptagonal tiling 74 {7,4}
Order-7 heptagonal tiling 77 {7,7}
Truncated order-7 triangular tiling 7.62 t{3,7}  
Truncated order-7 square tiling 7.82 t{4,7}
Truncated order-7 heptagonal tiling 7.142 t{7,7}
Octagonal tiling 83 {8,3}  
Order-4 octagonal tiling 84 {8,4}
Order-6 octagonal tiling 86 {8,6}
Order-8 octagonal tiling 88 {8,8}
Truncated order-8 hexagonal tiling 812 t{6,8}
Truncated order-8 triangular tiling 8.62 t{3,8}  
Truncated order-8 octagonal tiling 8.162 t{8,8}
Order-7 heptagrammic tiling (7/2)7 {7/2,7}
Order-3 apeirogonal tiling ∞3 {∞,3}  
Order-4 apeirogonal tiling ∞4 {∞,4}
Order-5 apeirogonal tiling ∞5 {∞,5}
Infinite-order apeirogonal tiling ∞∞ {∞,∞}
Truncated infinite-order triangular tiling ∞.62 t{3,∞}
Truncated infinite-order square tiling ∞.82 t{4,∞}

See also

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References

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