List of tessellations

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This is a list of tessellations.

Spherical

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-.svg
Spherical octahedron 34{3,4} Uniform tiling 432-t2.svg
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 Spherical (n=2, 3, ...)
Article Vertex configuration Schläfli symbol Image
Prism 4.4.nt{2, n}
= { }×{n}
Spherical hexagonal prism.svg { }×{6}
Antiprism 33.nsr{2,n}
= { }⊗{n}
Spherical hexagonal antiprism.svg { }⊗{6}
Dual semi-regular Spherical (n=2, 3, ...)
Article Vertex configuration Schläfli symbol Image
Bipyramid V42.ndt{2, n}
= { }+{n}
Spherical hexagonal bipyramid2.png { }+{6}
Trapezohedron V33.ndsr{2,n}
= { }⨁{n}
Spherical hexagonal trapezohedron.svg { }⨁{6}

Planar

Regular
ArticleVertex configurationSchläfli symbolImage
Apeirogonal hosohedron 2{2,∞} Apeirogonal hosohedron.svg
Order-2 apeirogonal tiling 2{∞,2} Apeirogonal tiling.svg
Square tiling 44{4,4} Square tiling uniform coloring 7.png
Triangular tiling 36{3,6} Uniform triangular tiling 121212.svg
Hexagonal tiling 63{6,3} Uniform tiling 63-t0.svg
Semi-regular
ArticleVertex configurationSchläfli symbolImage
Apeirogonal prism 42.∞t{2,∞} Infinite prism.svg
Apeirogonal antiprism 33.∞sr{2,∞} Infinite antiprism.svg
Snub square tiling 32.4.3.4s{4,4} Uniform tiling 44-snub.svg
Elongated triangular tiling 33.42{3,6}:e Elongated triangular tiling 2.png
Snub trihexagonal tiling 34.6sr{6,3} Tile 33336.svg
Rhombitrihexagonal tiling 3.4.6.4rr{6,3} Uniform tiling 63-t02.svg
Trihexagonal tiling 3.6.3.6r{6,3} Uniform tiling 63-t1.svg
Truncated hexagonal tiling 3.122t{6,3} Uniform tiling 63-t01.svg
Truncated trihexagonal tiling 4.6.12tr{6,3} Uniform tiling 63-t012.svg
Truncated square tiling 4.82tr{4,4} Uniform tiling 44-t01.svg
Dual semi-regular
ArticleFace configurationSchläfli symbolImage
Apeirogonal deltohedron V33.∞dsr{2,∞} Apeirogonal trapezohedron.svg
Apeirogonal bipyramid V42.∞dt{2,∞} Infinite bipyramid.svg
Cairo pentagonal tiling V32.4.3.4ds{4,4} 1-uniform 9 dual.svg
Prismatic pentagonal tiling V33.42d{3,6}:e 1-uniform 8 dual.svg
Floret pentagonal tiling V34.6dsr{6,3} 1-uniform 10 dual.svg
Deltoidal trihexagonal tiling V3.4.6.4drr{6,3} 1-uniform 6 dual.svg
Rhombille tiling V3.6.3.6dr{6,3} 1-uniform 7 dual.svg
Triakis triangular tiling V3.122dt{6,3} 1-uniform 4 dual.svg
Kisrhombille tiling V4.6.12dtr{6,3} 1-uniform 3 dual.svg
Tetrakis square tiling 4.82tr{4,4} 1-uniform 2 dual.svg

Hyperbolic

Hyperbolic
ArticleVertex configurationSchläfli symbolImage
Snub tetrapentagonal tiling 32.4.3.5sr{5,4} H2-5-4-snub.svg
Snub tetrahexagonal tiling 32.4.3.6sr{6,4} Uniform tiling 64-snub.png
Snub tetraheptagonal tiling 32.4.3.7sr{7,4} Uniform tiling 74-snub.png
Snub tetraoctagonal tiling 32.4.3.8sr{8,4} Uniform tiling 84-snub.png
Snub tetraapeirogonal tiling 32.4.3.∞sr{∞,4} Uniform tiling i42-snub.png
Snub pentapentagonal tiling 32.5.3.5s{5,4} Uniform tiling 552-snub.png
Snub pentahexagonal tiling 32.5.3.6sr{6,5} Uniform tiling 65-snub.png
Snub hexahexagonal tiling 32.6.3.6s{6,4} Uniform tiling 66-snub.png
Snub hexaoctagonal tiling 32.6.3.8sr{8,6} Uniform tiling 86-snub.png
Snub heptaheptagonal tiling 32.7.3.7sr{7,7} Uniform tiling 77-snub.png
Snub octaoctagonal tiling 32.8.3.8s{8,4} Uniform tiling 88-snub.png
Snub order-6 square tiling 33.4.3.4s{4,6} Uniform tiling 443-snub1.png
Snub apeiroapeirogonal tiling 32.∞.3.∞sr{∞,∞} Uniform tiling ii2-snub.png
Snub triheptagonal tiling 34.7sr{7,3} Snub triheptagonal tiling.svg
Snub trioctagonal tiling 34.8sr{8,3} H2-8-3-snub.svg
Snub triapeirogonal tiling 34.∞sr{∞,3} Uniform tiling i32-snub.png
Snub order-8 triangular tiling 35.4s{3,8} Uniform tiling 433-snub2.png
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 3.4.3.4.3.4h{8,3}
Alternated order-4 hexagonal tiling 3.4.3.4.3.4.3.4h{6,4}
Quarter order-6 square tiling 3.4.62.4q{4,6}
Rhombitriheptagonal tiling 3.4.7.4rr{7,3} Rhombitriheptagonal tiling.svg
Rhombitrioctagonal tiling 3.4.8.4rr{8,3} H2-8-3-cantellated.svg
Rhombitriapeirogonal tiling 3.4.∞.4rr{∞,3}
Cantic octagonal tiling 3.6.4.6h2{8,3}
Triheptagonal tiling 3.7.3.7r{7,3} Triheptagonal tiling.svg
Trioctagonal tiling 3.8.3.8r{8,3} H2-8-3-rectified.svg
Truncated heptagonal tiling 3.142t{7,3} Truncated heptagonal tiling.svg
Truncated octagonal tiling 3.162t{8,3} H2-8-3-trunc-dual.svg
Triapeirogonal tiling3.∞.3.∞r{∞,3} H2-i-3-rectified.png
Truncated order-3 apeirogonal tiling 3.∞2t{∞,3} H2 tiling 23i-3.png
Rhombitetrapentagonal tiling 42.5.4rr{5,4} H2-5-4-cantellated.svg
Rhombitetrahexagonal tiling 42.6.4rr{6,4}
Rhombitetraheptagonal tiling 42.7.4rr{7,4}
Rhombitetraoctagonal tiling 42.8.4rr{8,4}
Rhombitetraapeirogonal tiling 42.∞.4rr{∞,4}
Order-5 square tiling 45{4,5} H2-5-4-primal.svg
Order-6 square tiling 46{4,6} H2 tiling 246-4.png
Order-7 square tiling 47{4,7}
Order-8 square tiling 48{4,8}
Infinite-order square tiling 4{4,∞}
Tetrapentagonal tiling 4.5.4.5r{5,4} H2-5-4-rectified.svg
Tetrahexagonal tiling 4.6.4.6r{6,4}
Truncated trihexagonal tiling 4.6.12tr{6,3}
Truncated triheptagonal tiling 4.6.14tr{7,3} Truncated triheptagonal tiling.svg
Order 3-7 kisrhombille V4.6.14??? 3-7 kisrhombille.svg
Truncated trioctagonal tiling 4.6.16tr{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 4.7.4.7r{7,4}
Tetraoctagonal tiling 4.8.4.8r{8,4}
Truncated tetrapentagonal tiling 4.8.10tr{5,4} H2-5-4-omnitruncated.svg
4-5 kisrhombille V4.8.10??? H2-5-4-kisrhombille.svg
Truncated tetrahexagonal tiling 4.8.12tr{6,4}
Truncated tetraheptagonal tiling 4.8.14tr{7,4}
Truncated tetraoctagonal tiling 4.8.16tr{8,4}
Truncated tetraapeirogonal tiling 4.8.∞tr{∞,4}
Truncated order-4 pentagonal tiling 4.102t{5,4} H2-5-4-trunc-dual.svg
Truncated pentahexagonal tiling 4.10.12tr{6,5}
Truncated order-4 hexagonal tiling 4.122t{6,4}
Truncated hexaoctagonal tiling 4.12.16tr{8,6}
Truncated order-4 heptagonal tiling 4.142t{7,4}
Truncated order-4 octagonal tiling 4.162t{8,4}
Truncated order-4 apeirogonal tiling 4.∞2t{∞,4}
Tetraapeirogonal tiling4.∞.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 5.4.6.4rr{6,5}
Pentahexagonal tiling 5.6.5.6r{6,5}
Truncated order-5 square tiling 5.82t{4,5} H2-5-4-trunc-primal.svg
Truncated order-5 pentagonal tiling 5.102t{5,5}
Truncated order-5 hexagonal tiling 5.122t{6,5}
Pentaapeirogonal tiling5.∞.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 6.4.8.4rr{8,6}
Hexaoctagonal tiling 6.8.6.8r{8,6}
Truncated order-6 square tiling 6.82t{4,6}
Truncated order-6 pentagonal tiling 6.102t{5,6}
Truncated order-6 hexagonal tiling 6.122t{6,6}
Truncated order-6 octagonal tiling 6.162t{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 7.62t{3,7} Truncated order-7 triangular tiling.svg
Truncated order-7 square tiling 7.82t{4,7}
Truncated order-7 heptagonal tiling 7.142t{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 812t{6,8}
Truncated order-8 triangular tiling 8.62t{3,8} H2-8-3-trunc-primal.svg
Truncated order-8 octagonal tiling 8.162t{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 ∞.62t{3,∞}
Truncated infinite-order square tiling ∞.82t{4,∞}

See also

References