| 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 | | 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 | | 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,∞} | | |
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