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List of tessellations

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This is a list of tessellations.

This list is incomplete; you can help by adding missing items. (May 2021)

Spherical

Regular Spherical (n=1, 2, 3, ...)
Article Vertex configuration Schläfli symbol Image
Dihedron n {n,2} {6,2}
Hosohedron 2 {2,n} {2,6}
Spherical tetrahedron 3 {3,3}
Spherical octahedron 3 {3,4}
Spherical cube 4 {4,3}
Spherical icosahedron 3 {3,5}
Spherical dodecahedron 5 {5,3}
Semi-regular Spherical (n=2, 3, ...)
Article Vertex configuration Schläfli symbol Image
Prism 4.4.n t{2, n}
= { }×{n} 		{ }×{6}
Antiprism 3.n sr{2,n}
= { }⊗{n} 		{ }⊗{6}
Dual semi-regular Spherical (n=2, 3, ...)
Article Vertex configuration Schläfli symbol Image
Bipyramid V4.n dt{2, n}
= { }+{n} 		{ }+{6}
Trapezohedron V3.n dsr{2,n}
= { }⨁{n} 		{ }⨁{6}

Planar

Regular
Article Vertex configuration Schläfli symbol Image
Apeirogonal hosohedron 2 {2,∞}
Order-2 apeirogonal tiling ∞ {∞,2}
Square tiling 4 {4,4}
Triangular tiling 3 {3,6}
Hexagonal tiling 6 {6,3}
Semi-regular
Article Vertex configuration Schläfli symbol Image
Apeirogonal prism 4.∞ t{2,∞}
Apeirogonal antiprism 3.∞ sr{2,∞}
Snub square tiling 3.4.3.4 s{4,4}
Elongated triangular tiling 3.4 {3,6}:e
Snub trihexagonal tiling 3.6 sr{6,3}
Rhombitrihexagonal tiling 3.4.6.4 rr{6,3}
Trihexagonal tiling 3.6.3.6 r{6,3}
Truncated hexagonal tiling 3.12 t{6,3}
Truncated trihexagonal tiling 4.6.12 tr{6,3}
Truncated square tiling 4.8 tr{4,4}
Dual semi-regular
Article Face configuration Schläfli symbol Image
Apeirogonal deltohedron V3.∞ dsr{2,∞}
Apeirogonal bipyramid V4.∞ dt{2,∞}
Cairo pentagonal tiling V3.4.3.4 ds{4,4}
Prismatic pentagonal tiling V3.4 d{3,6}:e
Floret pentagonal tiling V3.6 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 V3.12 dt{6,3}
Kisrhombille tiling V4.6.12 dtr{6,3}
Tetrakis square tiling 4.8 tr{4,4}

Hyperbolic

Hyperbolic
Article Vertex configuration Schläfli symbol Image
Snub tetrapentagonal tiling 3.4.3.5 sr{5,4}
Snub tetrahexagonal tiling 3.4.3.6 sr{6,4}
Snub tetraheptagonal tiling 3.4.3.7 sr{7,4}
Snub tetraoctagonal tiling 3.4.3.8 sr{8,4}
Snub tetraapeirogonal tiling 3.4.3.∞ sr{∞,4}
Snub pentapentagonal tiling 3.5.3.5 s{5,4}
Snub pentahexagonal tiling 3.5.3.6 sr{6,5}
Snub hexahexagonal tiling 3.6.3.6 s{6,4}
Snub hexaoctagonal tiling 3.6.3.8 sr{8,6}
Snub heptaheptagonal tiling 3.7.3.7 sr{7,7}
Snub octaoctagonal tiling 3.8.3.8 s{8,4}
Snub order-6 square tiling 3.4.3.4 s{4,6}
Snub apeiroapeirogonal tiling 3.∞.3.∞ sr{∞,∞}
Snub triheptagonal tiling 3.7 sr{7,3}
Snub trioctagonal tiling 3.8 sr{8,3}
Snub triapeirogonal tiling 3.∞ sr{∞,3}
Snub order-8 triangular tiling 3.4 s{3,8}
Order-7 triangular tiling 3 {3,7}
Order-8 triangular tiling 3 {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 3.4.6.4 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 3.14 t{7,3}
Truncated octagonal tiling 3.16 t{8,3}
Triapeirogonal tiling 3.∞.3.∞ r{∞,3}
Truncated order-3 apeirogonal tiling 3.∞ t{∞,3}
Rhombitetrapentagonal tiling 4.5.4 rr{5,4}
Rhombitetrahexagonal tiling 4.6.4 rr{6,4}
Rhombitetraheptagonal tiling 4.7.4 rr{7,4}
Rhombitetraoctagonal tiling 4.8.4 rr{8,4}
Rhombitetraapeirogonal tiling 4.∞.4 rr{∞,4}
Order-5 square tiling 4 {4,5}
Order-6 square tiling 4 {4,6}
Order-7 square tiling 4 {4,7}
Order-8 square tiling 4 {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 4.10 t{5,4}
Truncated pentahexagonal tiling 4.10.12 tr{6,5}
Truncated order-4 hexagonal tiling 4.12 t{6,4}
Truncated hexaoctagonal tiling 4.12.16 tr{8,6}
Truncated order-4 heptagonal tiling 4.14 t{7,4}
Truncated order-4 octagonal tiling 4.16 t{8,4}
Truncated order-4 apeirogonal tiling 4.∞ t{∞,4}
Tetraapeirogonal tiling 4.∞.4.∞ r{∞,4}
Order-4 pentagonal tiling 5 {5,4}
Order-5 pentagonal tiling 5 {5,5}
Order-6 pentagonal tiling 5 {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 5.8 t{4,5}
Truncated order-5 pentagonal tiling 5.10 t{5,5}
Truncated order-5 hexagonal tiling 5.12 t{6,5}
Pentaapeirogonal tiling 5.∞.5.∞ r{∞,5}
Order-4 hexagonal tiling 6 {6,4}
Order-5 hexagonal tiling 6 {6,5}
Order-6 hexagonal tiling 6 {6,6}
Order-8 hexagonal tiling 6 {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 6.8 t{4,6}
Truncated order-6 pentagonal tiling 6.10 t{5,6}
Truncated order-6 hexagonal tiling 6.12 t{6,6}
Truncated order-6 octagonal tiling 6.16 t{8,6}
Heptagonal tiling 7 {7,3}
Order-4 heptagonal tiling 7 {7,4}
Order-7 heptagonal tiling 7 {7,7}
Truncated order-7 triangular tiling 7.6 t{3,7}
Truncated order-7 square tiling 7.8 t{4,7}
Truncated order-7 heptagonal tiling 7.14 t{7,7}
Octagonal tiling 8 {8,3}
Order-4 octagonal tiling 8 {8,4}
Order-6 octagonal tiling 8 {8,6}
Order-8 octagonal tiling 8 {8,8}
Truncated order-8 hexagonal tiling 8 t{6,8}
Truncated order-8 triangular tiling 8.6 t{3,8}
Truncated order-8 octagonal tiling 8.16 t{8,8}
Order-7 heptagrammic tiling (7/2) {7/2,7}
Order-3 apeirogonal tiling ∞ {∞,3}
Order-4 apeirogonal tiling ∞ {∞,4}
Order-5 apeirogonal tiling ∞ {∞,5}
Infinite-order apeirogonal tiling ∞ {∞,∞}
Truncated infinite-order triangular tiling ∞.6 t{3,∞}
Truncated infinite-order square tiling ∞.8 t{4,∞}

See also

References

Tessellation
Periodic


Aperiodic
Other
By vertex type
Spherical
Regular
Semi-
regular
Hyper-
bolic
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