List of tessellations explained

This is a list of tessellations.

Spherical

Regular Spherical (n=1, 2, 3, ...)
Article			Image
Dihedron	n^2
Hosohedron	2^n
Spherical tetrahedron	3^3
Spherical octahedron	3^4
Spherical cube	4^3
Spherical icosahedron	3^5
Spherical dodecahedron	5^3

Semi-regular Spherical (n=2, 3, ...)
Article			Image
Prism	4.4.n	t = ×	×
Antiprism	3^3.n	sr = ⊗	⊗

Dual semi-regular Spherical (n=2, 3, ...)
Article			Image
Bipyramid	V4^2.n	dt = +	+
Trapezohedron	V3^3.n	dsr = ⨁	⨁

Planar

Regular
Article	Vertex configuration	Schläfli symbol	Image
Apeirogonal hosohedron	2^∞
Order-2 apeirogonal tiling	∞^2
Square tiling	4^4
Triangular tiling	3^6
Hexagonal tiling	6^3

Semi-regular
Article	Vertex configuration	Schläfli symbol	Image
Apeirogonal prism	4^2.∞	t
Apeirogonal antiprism	3^3.∞	sr
Snub square tiling	3^2.4.3.4	s
Elongated triangular tiling	3^3.4^2	e
Snub trihexagonal tiling	3^4.6	sr
Rhombitrihexagonal tiling	3.4.6.4	rr
Trihexagonal tiling	3.6.3.6	r
Truncated hexagonal tiling	3.12^2	t
Truncated trihexagonal tiling	4.6.12	tr
Truncated square tiling	4.8^2	tr

Dual semi-regular
Article	Face configuration	Schläfli symbol	Image
Apeirogonal deltohedron	V3^3.∞	dsr
Apeirogonal bipyramid	V4^2.∞	dt
Cairo pentagonal tiling	V3^2.4.3.4	ds
Prismatic pentagonal tiling	V3^3.4^2	d:e
Floret pentagonal tiling	V3^4.6	dsr
Deltoidal trihexagonal tiling	V3.4.6.4	drr
Rhombille tiling	V3.6.3.6	dr
Triakis triangular tiling	V3.12^2	dt
Kisrhombille tiling	V4.6.12	dtr
Tetrakis square tiling	4.8^2	tr

Hyperbolic

Hyperbolic
Article	Vertex configuration	Schläfli symbol	Image
Snub tetrapentagonal tiling	3^2.4.3.5	sr
Snub tetrahexagonal tiling	3^2.4.3.6	sr
Snub tetraheptagonal tiling	3^2.4.3.7	sr
Snub tetraoctagonal tiling	3^2.4.3.8	sr
Snub tetraapeirogonal tiling	3^2.4.3.∞	sr
Snub pentapentagonal tiling	3^2.5.3.5	s
Snub pentahexagonal tiling	3^2.5.3.6	sr
Snub hexahexagonal tiling	3^2.6.3.6	s
Snub hexaoctagonal tiling	3^2.6.3.8	sr
Snub heptaheptagonal tiling	3^2.7.3.7	sr
Snub octaoctagonal tiling	3^2.8.3.8	s
Snub order-6 square tiling	3^3.4.3.4	s
Snub apeiroapeirogonal tiling	3^2.∞.3.∞	sr
Snub triheptagonal tiling	3^4.7	sr
Snub trioctagonal tiling	3^4.8	sr
Snub triapeirogonal tiling	3^4.∞	sr
Snub order-8 triangular tiling	3^5.4	s
Order-7 triangular tiling	3^7
Order-8 triangular tiling	3^8
Infinite-order triangular tiling	3^∞
Alternated octagonal tiling	3.4.3.4.3.4	h
Alternated order-4 hexagonal tiling	3.4.3.4.3.4.3.4	h
Quarter order-6 square tiling	3.4.6^2.4	q
Rhombitriheptagonal tiling	3.4.7.4	rr
Rhombitrioctagonal tiling	3.4.8.4	rr
Rhombitriapeirogonal tiling	3.4.∞.4	rr
Cantic octagonal tiling	3.6.4.6	h2
Triheptagonal tiling	3.7.3.7	r
Trioctagonal tiling	3.8.3.8	r
Truncated heptagonal tiling	3.14^2	t
Truncated octagonal tiling	3.16^2	t
Triapeirogonal tiling	3.∞.3.∞	r
Truncated order-3 apeirogonal tiling	3.∞^2	t
Rhombitetrapentagonal tiling	4^2.5.4	rr
Rhombitetrahexagonal tiling	4^2.6.4	rr
Rhombitetraheptagonal tiling	4^2.7.4	rr
Rhombitetraoctagonal tiling	4^2.8.4	rr
Rhombitetraapeirogonal tiling	4^2.∞.4	rr
Order-5 square tiling	4^5
Order-6 square tiling	4^6
Order-7 square tiling	4^7
Order-8 square tiling	4^8
Infinite-order square tiling	4^∞
Tetrapentagonal tiling	4.5.4.5	r
Tetrahexagonal tiling	4.6.4.6	r
Truncated trihexagonal tiling	4.6.12	tr
Truncated triheptagonal tiling	4.6.14	tr
Order 3-7 kisrhombille	V4.6.14	???
Truncated trioctagonal tiling	4.6.16	tr
Order 3-8 kisrhombille	V4.6.16	???
Truncated triapeirogonal tiling	4.6.∞	tr
Tetraheptagonal tiling	4.7.4.7	r
Tetraoctagonal tiling	4.8.4.8	r
Truncated tetrapentagonal tiling	4.8.10	tr
4-5 kisrhombille	V4.8.10	???
Truncated tetrahexagonal tiling	4.8.12	tr
Truncated tetraheptagonal tiling	4.8.14	tr
Truncated tetraoctagonal tiling	4.8.16	tr
Truncated tetraapeirogonal tiling	4.8.∞	tr
Truncated order-4 pentagonal tiling	4.10^2	t
Truncated pentahexagonal tiling	4.10.12	tr
Truncated order-4 hexagonal tiling	4.12^2	t
Truncated hexaoctagonal tiling	4.12.16	tr
Truncated order-4 heptagonal tiling	4.14^2	t
Truncated order-4 octagonal tiling	4.16^2	t
Truncated order-4 apeirogonal tiling	4.∞^2	t
Tetraapeirogonal tiling	4.∞.4.∞	r
Order-4 pentagonal tiling	5^4
Order-5 pentagonal tiling	5^5
Order-6 pentagonal tiling	5^6
Infinite-order pentagonal tiling	5^∞
Rhombipentahexagonal tiling	5.4.6.4	rr
Pentahexagonal tiling	5.6.5.6	r
Truncated order-5 square tiling	5.8^2	t
Truncated order-5 pentagonal tiling	5.10^2	t
Truncated order-5 hexagonal tiling	5.12^2	t
Pentaapeirogonal tiling	5.∞.5.∞	r
Order-4 hexagonal tiling	6^4
Order-5 hexagonal tiling	6^5
Order-6 hexagonal tiling	6^6
Order-8 hexagonal tiling	6^8
Rhombihexaoctagonal tiling	6.4.8.4	rr
Hexaoctagonal tiling	6.8.6.8	r
Truncated order-6 square tiling	6.8^2	t
Truncated order-6 pentagonal tiling	6.10^2	t
Truncated order-6 hexagonal tiling	6.12^2	t
Truncated order-6 octagonal tiling	6.16^2	t
Heptagonal tiling	7^3
Order-4 heptagonal tiling	7^4
Order-7 heptagonal tiling	7^7
Truncated order-7 triangular tiling	7.6^2	t
Truncated order-7 square tiling	7.8^2	t
Truncated order-7 heptagonal tiling	7.14^2	t
Octagonal tiling	8^3
Order-4 octagonal tiling	8^4
Order-6 octagonal tiling	8^6
Order-8 octagonal tiling	8^8
Truncated order-8 hexagonal tiling	8^12	t
Truncated order-8 triangular tiling	8.6^2	t
Truncated order-8 octagonal tiling	8.16^2	t
Order-7 heptagrammic tiling	(7/2)^7
Order-3 apeirogonal tiling	∞^3
Order-4 apeirogonal tiling	∞^4
Order-5 apeirogonal tiling	∞^5
Infinite-order apeirogonal tiling	∞^∞
Truncated infinite-order triangular tiling	∞.6^2	t
Truncated infinite-order square tiling	∞.8^2	t

See also

• Uniform tiling
  • Convex uniform honeycombs
  • List of k-uniform tilings
  • List of Euclidean uniform tilings
  • Uniform tilings in hyperbolic plane