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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}

Regular
Article	Vertex configuration	Schläfli symbol	Image
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
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,∞}

Other
Anisohedral and Isohedral Architectonic and catoptric Circle Limit III Computer graphics Honeycomb Isotoxal List Packing Problems Domino Wang Heesch's Squaring Dividing a square into similar rectangles Prototile Conway criterion Girih Regular Division of the Plane Regular grid Substitution Voronoi Voderberg

By vertex type

Spherical	2ⁿ 3³.n V3³.n 4².n V4².n
Regular	2^∞ 3⁶ 4⁴ 6³
Semi- regular	3².4.3.4 V3².4.3.4 3³.4² 3³.∞ 3⁴.6 V3⁴.6 3.4.6.4 (3.6)² 3.12² 4².∞ 4.6.12 4.8²
Hyper- bolic	3².4.3.5 3².4.3.6 3².4.3.7 3².4.3.8 3².4.3.∞ 3².5.3.5 3².5.3.6 3².6.3.6 3².6.3.8 3².7.3.7 3².8.3.8 3³.4.3.4 3².∞.3.∞ 3⁴.7 3⁴.8 3⁴.∞ 3⁵.4 3⁷ 3⁸ 3^∞ (3.4)³ (3.4)⁴ 3.4.6².4 3.4.7.4 3.4.8.4 3.4.∞.4 3.6.4.6 (3.7)² (3.8)² 3.14² 3.16² 3.∞² 4².5.4 4².6.4 4².7.4 4².8.4 4².∞.4 4⁵ 4⁶ 4⁷ 4⁸ 4^∞ (4.5)² (4.6)² 4.6.12 4.6.14 V4.6.14 4.6.16 V4.6.16 4.6.∞ (4.7)² (4.8)² 4.8.10 V4.8.10 4.8.12 4.8.14 4.8.16 4.8.∞ 4.10² 4.10.12 4.12² 4.12.16 4.14² 4.16² 4.∞² 5⁴ 5⁵ 5⁶ 5^∞ 5.4.6.4 (5.6)² 5.8² 5.10² 5.12² 6⁴ 6⁵ 6⁶ 6⁸ 6.4.8.4 (6.8)² 6.8² 6.10² 6.12² 6.16² 7³ 7⁴ 7⁷ 7.6² 7.8² 7.14² 8³ 8⁴ 8⁶ 8⁸ 8.6² 8.12² 8.16² ∞³ ∞⁴ ∞⁵ ∞^∞ ∞.6² ∞.8²

See also