# List of tessellations

This is a list of tessellations.

## Spherical

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

## Planar

Regular :
| Article | Vertex configuration | Schläfli symbol |
| Apeirogonal hosohedron | 2$^∞$ | {2,∞} |
| Order-2 apeirogonal tiling | ∞$^2$ | {∞,2} |
| Square tiling | 4$^4$ | {4,4} |
| Triangular tiling | 3$^6$ | {3,6} |
| Hexagonal tiling | 6$^3$ | {6,3} |
Semi-regular :
| Article | Vertex configuration | Schläfli symbol |
| Apeirogonal prism | 4$^2$.∞ | t{2,∞} |
| Apeirogonal antiprism | 3$^3$.∞ | sr{2,∞} |
| Snub square tiling | 3$^2$.4.3.4 | s{4,4} |
| Elongated triangular tiling | 3$^3$.4$^2$ | {3,6}:e |
| Snub trihexagonal tiling | 3$^4$.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$^2$ | t{6,3} |
| Truncated trihexagonal tiling | 4.6.12 | tr{6,3} |
| Truncated square tiling | 4.8$^2$ | tr{4,4} |
Dual semi-regular :
| Article | Face configuration | Schläfli symbol |
| Apeirogonal deltohedron | V3$^3$.∞ | dsr{2,∞} |
| Apeirogonal bipyramid | V4$^2$.∞ | dt{2,∞} |
| Cairo pentagonal tiling | V3$^2$.4.3.4 | ds{4,4} |
| Prismatic pentagonal tiling | V3$^3$.4$^2$ | d{3,6}:e |
| Floret pentagonal tiling | V3$^4$.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$^2$ | dt{6,3} |
| Kisrhombille tiling | V4.6.12 | dtr{6,3} |
| Tetrakis square tiling | 4.8$^2$ | tr{4,4} |

## Hyperbolic

Hyperbolic :
| Article | Vertex configuration | Schläfli symbol |
| Snub tetrapentagonal tiling | 3$^2$.4.3.5 | sr{5,4} |
| Snub tetrahexagonal tiling | 3$^2$.4.3.6 | sr{6,4} |
| Snub tetraheptagonal tiling | 3$^2$.4.3.7 | sr{7,4} |
| Snub tetraoctagonal tiling | 3$^2$.4.3.8 | sr{8,4} |
| Snub tetraapeirogonal tiling | 3$^2$.4.3.∞ | sr{∞,4} |
| Snub pentapentagonal tiling | 3$^2$.5.3.5 | s{5,4} |
| Snub pentahexagonal tiling | 3$^2$.5.3.6 | sr{6,5} |
| Snub hexahexagonal tiling | 3$^2$.6.3.6 | s{6,4} |
| Snub hexaoctagonal tiling | 3$^2$.6.3.8 | sr{8,6} |
| Snub heptaheptagonal tiling | 3$^2$.7.3.7 | sr{7,7} |
| Snub octaoctagonal tiling | 3$^2$.8.3.8 | s{8,4} |
| Snub order-6 square tiling | 3$^3$.4.3.4 | s{4,6} |
| Snub apeiroapeirogonal tiling | 3$^2$.∞.3.∞ | sr{∞,∞} |
| Snub triheptagonal tiling | 3$^4$.7 | sr{7,3} |
| Snub trioctagonal tiling | 3$^4$.8 | sr{8,3} |
| Snub triapeirogonal tiling | 3$^4$.∞ | sr{∞,3} |
| Snub order-8 triangular tiling | 3$^5$.4 | s{3,8} |
| Order-7 triangular tiling | 3$^7$ | {3,7} |
| Order-8 triangular tiling | 3$^8$ | {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$^2$.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 | h$_2${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$^2$ | t{7,3} |
| Truncated octagonal tiling | 3.16$^2$ | t{8,3} |
| Triapeirogonal tiling | 3.∞.3.∞ | r{∞,3} |
| Truncated order-3 apeirogonal tiling | 3.∞$^2$ | t{∞,3} |
| Rhombitetrapentagonal tiling | 4$^2$.5.4 | rr{5,4} |
| Rhombitetrahexagonal tiling | 4$^2$.6.4 | rr{6,4} |
| Rhombitetraheptagonal tiling | 4$^2$.7.4 | rr{7,4} |
| Rhombitetraoctagonal tiling | 4$^2$.8.4 | rr{8,4} |
| Rhombitetraapeirogonal tiling | 4$^2$.∞.4 | rr{∞,4} |
| Order-5 square tiling | 4$^5$ | {4,5} |
| Order-6 square tiling | 4$^6$ | {4,6} |
| Order-7 square tiling | 4$^7$ | {4,7} |
| Order-8 square tiling | 4$^8$ | {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$^2$ | t{5,4} |
| Truncated pentahexagonal tiling | 4.10.12 | tr{6,5} |
| Truncated order-4 hexagonal tiling | 4.12$^2$ | t{6,4} |
| Truncated hexaoctagonal tiling | 4.12.16 | tr{8,6} |
| Truncated order-4 heptagonal tiling | 4.14$^2$ | t{7,4} |
| Truncated order-4 octagonal tiling | 4.16$^2$ | t{8,4} |
| Truncated order-4 apeirogonal tiling | 4.∞$^2$ | t{∞,4} |
| Tetraapeirogonal tiling | 4.∞.4.∞ | r{∞,4} |
| Order-4 pentagonal tiling | 5$^4$ | {5,4} |
| Order-5 pentagonal tiling | 5$^5$ | {5,5} |
| Order-6 pentagonal tiling | 5$^6$ | {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$^2$ | t{4,5} |
| Truncated order-5 pentagonal tiling | 5.10$^2$ | t{5,5} |
| Truncated order-5 hexagonal tiling | 5.12$^2$ | t{6,5} |
| Pentaapeirogonal tiling | 5.∞.5.∞ | r{∞,5} |
| Order-4 hexagonal tiling | 6$^4$ | {6,4} |
| Order-5 hexagonal tiling | 6$^5$ | {6,5} |
| Order-6 hexagonal tiling | 6$^6$ | {6,6} |
| Order-8 hexagonal tiling | 6$^8$ | {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$^2$ | t{4,6} |
| Truncated order-6 pentagonal tiling | 6.10$^2$ | t{5,6} |
| Truncated order-6 hexagonal tiling | 6.12$^2$ | t{6,6} |
| Truncated order-6 octagonal tiling | 6.16$^2$ | t{8,6} |
| Heptagonal tiling | 7$^3$ | {7,3} |
| Order-4 heptagonal tiling | 7$^4$ | {7,4} |
| Order-7 heptagonal tiling | 7$^7$ | {7,7} |
| Truncated order-7 triangular tiling | 7.6$^2$ | t{3,7} |
| Truncated order-7 square tiling | 7.8$^2$ | t{4,7} |
| Truncated order-7 heptagonal tiling | 7.14$^2$ | t{7,7} |
| Octagonal tiling | 8$^3$ | {8,3} |
| Order-4 octagonal tiling | 8$^4$ | {8,4} |
| Order-6 octagonal tiling | 8$^6$ | {8,6} |
| Order-8 octagonal tiling | 8$^8$ | {8,8} |
| Truncated order-8 hexagonal tiling | 8$^{12}$ | t{6,8} |
| Truncated order-8 triangular tiling | 8.6$^2$ | t{3,8} |
| Truncated order-8 octagonal tiling | 8.16$^2$ | 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 | ∞.6$^2$ | t{3,∞} |
| Truncated infinite-order square tiling | ∞.8$^2$ | t{4,∞} |