List of tessellations – Wikipedia

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Regular Spherical (n=1, 2, 3, …)
Article Vertex configuration Schläfli symbol Image
Dihedron n2 {n,2} Hexagonal dihedron.png {6,2}
Hosohedron 2n {2,n} Spherical hexagonal hosohedron2.png {2,6}
Spherical tetrahedron 33 {3,3} Uniform tiling 332-t0-1-.png
Spherical octahedron 34 {3,4} Uniform tiling 432-t2.png
Spherical cube 43 {4,3} Uniform tiling 432-t0.png
Spherical icosahedron 35 {3,5} Uniform tiling 532-t2.png
Spherical dodecahedron 53 {5,3} Uniform tiling 532-t0.png
Semi-regular
Article Vertex configuration Schläfli symbol Image
Apeirogonal prism 42.∞ t{2,∞} Infinite prism.svg
Apeirogonal antiprism 33.∞ sr{2,∞} Infinite antiprism.svg
Snub square tiling 32.4.3.4 s{4,4} Uniform tiling 44-snub.png
Elongated triangular tiling 33.42 {3,6}:e Elongated triangular tiling 2.png
Snub trihexagonal tiling 34.6 sr{6,3} Tile 33336.svg
Rhombitrihexagonal tiling 3.4.6.4 rr{6,3} Uniform tiling 63-t02.svg
Trihexagonal tiling 3.6.3.6 r{6,3} Uniform tiling 63-t1.svg
Truncated hexagonal tiling 3.122 t{6,3} Uniform tiling 63-t01.svg
Truncated trihexagonal tiling 4.6.12 tr{6,3} Uniform tiling 63-t012.svg
Truncated square tiling 4.82 tr{4,4} Uniform tiling 44-t01.svg
Dual semi-regular
Article Face configuration Schläfli symbol Image
Apeirogonal deltohedron V33.∞ dsr{2,∞} Apeirogonal trapezohedron.svg
Apeirogonal bipyramid V42.∞ dt{2,∞} Infinite bipyramid.svg
Cairo pentagonal tiling V32.4.3.4 ds{4,4} 1-uniform 9 dual.svg
Prismatic pentagonal tiling V33.42 d{3,6}:e 1-uniform 8 dual.svg
Floret pentagonal tiling V34.6 dsr{6,3} 1-uniform 10 dual.svg
Deltoidal trihexagonal tiling V3.4.6.4 drr{6,3} 1-uniform 6 dual.svg
Rhombille tiling V3.6.3.6 dr{6,3} 1-uniform 7 dual.svg
Triakis triangular tiling V3.122 dt{6,3} 1-uniform 4 dual.svg
Kisrhombille tiling V4.6.12 dtr{6,3} 1-uniform 3 dual.svg
Tetrakis square tiling 4.82 tr{4,4} 1-uniform 2 dual.svg
Hyperbolic
Article Vertex configuration Schläfli symbol Image
Snub tetrapentagonal tiling 32.4.3.5 sr{5,4} H2-5-4-snub.svg
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 triheptagonal tiling.svg
Snub trioctagonal tiling 34.8 sr{8,3} H2-8-3-snub.svg
Snub triapeirogonal tiling 34.∞ sr{∞,3}
Snub order-8 triangular tiling 35.4 s{3,8}
Order-7 triangular tiling 37 {3,7} Order-7 triangular tiling.svg
Order-8 triangular tiling 38 {3,8} H2-8-3-primal.svg
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} Rhombitriheptagonal tiling.svg
Rhombitrioctagonal tiling 3.4.8.4 rr{8,3} H2-8-3-cantellated.svg
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} Triheptagonal tiling.svg
Trioctagonal tiling 3.8.3.8 r{8,3} H2-8-3-rectified.svg
Truncated heptagonal tiling 3.142 t{7,3} Truncated heptagonal tiling.svg
Truncated octagonal tiling 3.162 t{8,3} H2-8-3-trunc-dual.svg
Triapeirogonal tiling 3.∞.3.∞ r{∞,3}
Truncated order-3 apeirogonal tiling 3.∞2 t{∞,3}
Rhombitetrapentagonal tiling 42.5.4 rr{5,4} H2-5-4-cantellated.svg
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} H2-5-4-primal.svg
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} H2-5-4-rectified.svg
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} Truncated triheptagonal tiling.svg
Order 3-7 kisrhombille V4.6.14 ??? 3-7 kisrhombille.svg
Truncated trioctagonal tiling 4.6.16 tr{8,3} H2-8-3-omnitruncated.svg
Order 3-8 kisrhombille V4.6.16 ??? H2-8-3-kisrhombille.svg
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} H2-5-4-omnitruncated.svg
4-5 kisrhombille V4.8.10 ??? H2-5-4-kisrhombille.svg
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} H2-5-4-trunc-dual.svg
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} H2-5-4-dual.svg
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} H2-5-4-trunc-primal.svg
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} Heptagonal tiling.svg
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 triangular tiling.svg
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} H2-8-3-dual.svg
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} H2-8-3-trunc-primal.svg
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} H2-I-3-dual.svg
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,∞}
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