Regular Spherical (n=1, 2, 3, ...)
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Article |
Vertex configuration |
Schläfli symbol |
Image
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Dihedron
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n2
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{n,2}
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{6,2}
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Hosohedron
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2n
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{2,n}
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{2,6}
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Spherical tetrahedron
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33
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{3,3}
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Spherical octahedron
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34
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{3,4}
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Spherical cube
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43
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{4,3}
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Spherical icosahedron
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35
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{3,5}
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Spherical dodecahedron
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53
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{5,3}
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Semi-regular
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Article |
Vertex configuration |
Schläfli symbol |
Image
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Apeirogonal prism
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42.∞
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t{2,∞}
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Apeirogonal antiprism
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33.∞
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sr{2,∞}
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Snub square tiling
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32.4.3.4
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s{4,4}
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Elongated triangular tiling
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33.42
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{3,6}:e
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Snub trihexagonal tiling
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34.6
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sr{6,3}
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Rhombitrihexagonal tiling
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3.4.6.4
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rr{6,3}
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Trihexagonal tiling
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3.6.3.6
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r{6,3}
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Truncated hexagonal tiling
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3.122
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t{6,3}
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Truncated trihexagonal tiling
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4.6.12
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tr{6,3}
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Truncated square tiling
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4.82
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tr{4,4}
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Dual semi-regular
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Article |
Face configuration |
Schläfli symbol |
Image
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Apeirogonal deltohedron
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V33.∞
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dsr{2,∞}
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Apeirogonal bipyramid
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V42.∞
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dt{2,∞}
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Cairo pentagonal tiling
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V32.4.3.4
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ds{4,4}
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Prismatic pentagonal tiling
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V33.42
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d{3,6}:e
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Floret pentagonal tiling
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V34.6
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dsr{6,3}
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Deltoidal trihexagonal tiling
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V3.4.6.4
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drr{6,3}
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Rhombille tiling
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V3.6.3.6
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dr{6,3}
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Triakis triangular tiling
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V3.122
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dt{6,3}
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Kisrhombille tiling
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V4.6.12
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dtr{6,3}
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Tetrakis square tiling
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4.82
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tr{4,4}
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Hyperbolic
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Article |
Vertex configuration |
Schläfli symbol |
Image
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Snub tetrapentagonal tiling
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32.4.3.5
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sr{5,4}
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Snub tetrahexagonal tiling
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32.4.3.6
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sr{6,4}
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Snub tetraheptagonal tiling
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32.4.3.7
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sr{7,4}
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Snub tetraoctagonal tiling
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32.4.3.8
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sr{8,4}
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Snub tetraapeirogonal tiling
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32.4.3.∞
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sr{∞,4}
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Snub pentapentagonal tiling
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32.5.3.5
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s{5,4}
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Snub pentahexagonal tiling
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32.5.3.6
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sr{6,5}
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Snub hexahexagonal tiling
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32.6.3.6
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s{6,4}
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Snub hexaoctagonal tiling
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32.6.3.8
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sr{8,6}
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Snub heptaheptagonal tiling
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32.7.3.7
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sr{7,7}
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Snub octaoctagonal tiling
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32.8.3.8
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s{8,4}
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Snub order-6 square tiling
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33.4.3.4
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s{4,6}
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Snub apeiroapeirogonal tiling
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32.∞.3.∞
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sr{∞,∞}
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Snub triheptagonal tiling
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34.7
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sr{7,3}
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Snub trioctagonal tiling
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34.8
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sr{8,3}
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Snub triapeirogonal tiling
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34.∞
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sr{∞,3}
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Snub order-8 triangular tiling
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35.4
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s{3,8}
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Order-7 triangular tiling
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37
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{3,7}
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Order-8 triangular tiling
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38
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{3,8}
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Infinite-order triangular tiling
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3∞
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{3,∞}
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Alternated octagonal tiling
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3.4.3.4.3.4
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h{8,3}
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Alternated order-4 hexagonal tiling
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3.4.3.4.3.4.3.4
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h{6,4}
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Quarter order-6 square tiling
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3.4.62.4
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q{4,6}
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Rhombitriheptagonal tiling
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3.4.7.4
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rr{7,3}
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Rhombitrioctagonal tiling
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3.4.8.4
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rr{8,3}
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Rhombitriapeirogonal tiling
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3.4.∞.4
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rr{∞,3}
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Cantic octagonal tiling
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3.6.4.6
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h2{8,3}
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Triheptagonal tiling
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3.7.3.7
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r{7,3}
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Trioctagonal tiling
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3.8.3.8
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r{8,3}
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Truncated heptagonal tiling
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3.142
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t{7,3}
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Truncated octagonal tiling
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3.162
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t{8,3}
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Triapeirogonal tiling
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3.∞.3.∞
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r{∞,3}
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Truncated order-3 apeirogonal tiling
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3.∞2
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t{∞,3}
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Rhombitetrapentagonal tiling
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42.5.4
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rr{5,4}
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Rhombitetrahexagonal tiling
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42.6.4
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rr{6,4}
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Rhombitetraheptagonal tiling
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42.7.4
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rr{7,4}
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Rhombitetraoctagonal tiling
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42.8.4
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rr{8,4}
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Rhombitetraapeirogonal tiling
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42.∞.4
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rr{∞,4}
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Order-5 square tiling
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45
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{4,5}
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Order-6 square tiling
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46
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{4,6}
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Order-7 square tiling
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47
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{4,7}
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Order-8 square tiling
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48
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{4,8}
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Infinite-order square tiling
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4∞
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{4,∞}
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Tetrapentagonal tiling
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4.5.4.5
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r{5,4}
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Tetrahexagonal tiling
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4.6.4.6
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r{6,4}
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Truncated trihexagonal tiling
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4.6.12
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tr{6,3}
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Truncated triheptagonal tiling
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4.6.14
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tr{7,3}
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Order 3-7 kisrhombille
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V4.6.14
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???
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Truncated trioctagonal tiling
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4.6.16
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tr{8,3}
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Order 3-8 kisrhombille
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V4.6.16
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???
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Truncated triapeirogonal tiling
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4.6.∞
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tr{∞,3}
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Tetraheptagonal tiling
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4.7.4.7
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r{7,4}
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Tetraoctagonal tiling
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4.8.4.8
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r{8,4}
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Truncated tetrapentagonal tiling
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4.8.10
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tr{5,4}
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4-5 kisrhombille
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V4.8.10
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???
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Truncated tetrahexagonal tiling
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4.8.12
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tr{6,4}
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Truncated tetraheptagonal tiling
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4.8.14
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tr{7,4}
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Truncated tetraoctagonal tiling
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4.8.16
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tr{8,4}
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Truncated tetraapeirogonal tiling
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4.8.∞
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tr{∞,4}
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Truncated order-4 pentagonal tiling
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4.102
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t{5,4}
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Truncated pentahexagonal tiling
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4.10.12
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tr{6,5}
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Truncated order-4 hexagonal tiling
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4.122
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t{6,4}
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Truncated hexaoctagonal tiling
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4.12.16
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tr{8,6}
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Truncated order-4 heptagonal tiling
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4.142
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t{7,4}
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Truncated order-4 octagonal tiling
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4.162
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t{8,4}
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Truncated order-4 apeirogonal tiling
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4.∞2
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t{∞,4}
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Tetraapeirogonal tiling
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4.∞.4.∞
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r{∞,4}
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Order-4 pentagonal tiling
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54
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{5,4}
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Order-5 pentagonal tiling
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55
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{5,5}
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Order-6 pentagonal tiling
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56
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{5,6}
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Infinite-order pentagonal tiling
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5∞
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{5,∞}
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Rhombipentahexagonal tiling
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5.4.6.4
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rr{6,5}
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Pentahexagonal tiling
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5.6.5.6
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r{6,5}
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Truncated order-5 square tiling
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5.82
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t{4,5}
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Truncated order-5 pentagonal tiling
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5.102
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t{5,5}
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Truncated order-5 hexagonal tiling
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5.122
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t{6,5}
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Pentaapeirogonal tiling
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5.∞.5.∞
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r{∞,5}
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Order-4 hexagonal tiling
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64
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{6,4}
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Order-5 hexagonal tiling
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65
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{6,5}
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Order-6 hexagonal tiling
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66
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{6,6}
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Order-8 hexagonal tiling
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68
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{6,8}
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Rhombihexaoctagonal tiling
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6.4.8.4
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rr{8,6}
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Hexaoctagonal tiling
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6.8.6.8
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r{8,6}
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Truncated order-6 square tiling
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6.82
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t{4,6}
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Truncated order-6 pentagonal tiling
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6.102
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t{5,6}
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Truncated order-6 hexagonal tiling
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6.122
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t{6,6}
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Truncated order-6 octagonal tiling
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6.162
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t{8,6}
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Heptagonal tiling
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73
|
{7,3}
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Order-4 heptagonal tiling
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74
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{7,4}
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Order-7 heptagonal tiling
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77
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{7,7}
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Truncated order-7 triangular tiling
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7.62
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t{3,7}
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Truncated order-7 square tiling
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7.82
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t{4,7}
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Truncated order-7 heptagonal tiling
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7.142
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t{7,7}
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Octagonal tiling
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83
|
{8,3}
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Order-4 octagonal tiling
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84
|
{8,4}
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Order-6 octagonal tiling
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86
|
{8,6}
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Order-8 octagonal tiling
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88
|
{8,8}
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Truncated order-8 hexagonal tiling
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812
|
t{6,8}
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Truncated order-8 triangular tiling
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8.62
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t{3,8}
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Truncated order-8 octagonal tiling
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8.162
|
t{8,8}
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Order-7 heptagrammic tiling
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(7/2)7
|
{7/2,7}
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Order-3 apeirogonal tiling
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∞3
|
{∞,3}
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Order-4 apeirogonal tiling
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∞4
|
{∞,4}
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Order-5 apeirogonal tiling
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∞5
|
{∞,5}
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Infinite-order apeirogonal tiling
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∞∞
|
{∞,∞}
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Truncated infinite-order triangular tiling
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∞.62
|
t{3,∞}
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Truncated infinite-order square tiling
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∞.82
|
t{4,∞}
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