This is a list of tessellations.
Spherical 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 Regular Article Vertex configuration Schläfli symbol Imagereference 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 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 Tessellation Uniform tiling Convex uniform honeycombs List of k-uniform tilings List of Euclidean uniform tilings Uniform tilings in hyperbolic plane
References