List of tessellations
Regular
Spherical
(
n
=1, 2, 3, ...)
Article
Vertex configuration
Schläfli symbol
Image
Dihedron
n
2
{n,2}
{6,2}
Hosohedron
2
n
{2,n}
{2,6}
Spherical tetrahedron
3
3
{3,3}
Spherical octahedron
3
4
{3,4}
Spherical cube
4
3
{4,3}
Spherical icosahedron
3
5
{3,5}
Spherical dodecahedron
5
3
{5,3}
Semi-regular
Spherical
(
n
=2, 3, ...)
Article
Vertex configuration
Schläfli symbol
Image
Prism
4.4.n
t{2, n}
= {
}×{n}
{
}×{6}
Antiprism
3
3
.n
sr{2,n}
= {
}⊗{n}
{
}⊗{6}
Dual semi-regular
Spherical
(
n
=2, 3, ...)
Article
Vertex configuration
Schläfli symbol
Image
Bipyramid
V4
2
.n
dt{2, n}
= {
}+{n}
{
}+{6}
Trapezohedron
V3
3
.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
4
4
{4,4}
Triangular tiling
3
6
{3,6}
Hexagonal tiling
6
3
{6,3}
Semi-regular
Article
Vertex configuration
Schläfli symbol
Image
Apeirogonal prism
4
2
.∞
t{2,∞}
Apeirogonal antiprism
3
3
.∞
sr{2,∞}
Snub square tiling
3
2
.4.3.4
s{4,4}
Elongated triangular tiling
3
3
.4
2
{3,6}:e
Snub trihexagonal tiling
3
4
.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
3.12
2
t{6,3}
Truncated trihexagonal tiling
4.6.12
tr{6,3}
Truncated square tiling
4.8
2
tr{4,4}
Dual semi-regular
Article
Face configuration
Schläfli symbol
Image
Apeirogonal deltohedron
V3
3
.∞
dsr{2,∞}
Apeirogonal bipyramid
V4
2
.∞
dt{2,∞}
Cairo pentagonal tiling
V3
2
.4.3.4
ds{4,4}
Prismatic pentagonal tiling
V3
3
.4
2
d{3,6}:e
Floret pentagonal tiling
V3
4
.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
V3.12
2
dt{6,3}
Kisrhombille tiling
V4.6.12
dtr{6,3}
Tetrakis square tiling
4.8
2
tr{4,4}
Hyperbolic
Article
Vertex configuration
Schläfli symbol
Image
Snub tetrapentagonal tiling
3
2
.4.3.5
sr{5,4}
Snub tetrahexagonal tiling
3
2
.4.3.6
sr{6,4}
Snub tetraheptagonal tiling
3
2
.4.3.7
sr{7,4}
Snub tetraoctagonal tiling
3
2
.4.3.8
sr{8,4}
Snub tetraapeirogonal tiling
3
2
.4.3.∞
sr{∞,4}
Snub pentapentagonal tiling
3
2
.5.3.5
s{5,4}
Snub pentahexagonal tiling
3
2
.5.3.6
sr{6,5}
Snub hexahexagonal tiling
3
2
.6.3.6
s{6,4}
Snub hexaoctagonal tiling
3
2
.6.3.8
sr{8,6}
Snub heptaheptagonal tiling
3
2
.7.3.7
sr{7,7}
Snub octaoctagonal tiling
3
2
.8.3.8
s{8,4}
Snub order-6 square tiling
3
3
.4.3.4
s{4,6}
Snub apeiroapeirogonal tiling
3
2
.∞.3.∞
sr{∞,∞}
Snub triheptagonal tiling
3
4
.7
sr{7,3}
Snub trioctagonal tiling
3
4
.8
sr{8,3}
Snub triapeirogonal tiling
3
4
.∞
sr{∞,3}
Snub order-8 triangular tiling
3
5
.4
s{3,8}
Order-7 triangular tiling
3
7
{3,7}
Order-8 triangular tiling
3
8
{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
3.4.6
2
.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
h
2
{8,3}
Triheptagonal tiling
3.7.3.7
r{7,3}
Trioctagonal tiling
3.8.3.8
r{8,3}
Truncated heptagonal tiling
3.14
2
t{7,3}
Truncated octagonal tiling
3.16
2
t{8,3}
Triapeirogonal tiling
3.∞.3.∞
r{∞,3}
Truncated order-3 apeirogonal tiling
3.∞
2
t{∞,3}
Rhombitetrapentagonal tiling
4
2
.5.4
rr{5,4}
Rhombitetrahexagonal tiling
4
2
.6.4
rr{6,4}
Rhombitetraheptagonal tiling
4
2
.7.4
rr{7,4}
Rhombitetraoctagonal tiling
4
2
.8.4
rr{8,4}
Rhombitetraapeirogonal tiling
4
2
.∞.4
rr{∞,4}
Order-5 square tiling
4
5
{4,5}
Order-6 square tiling
4
6
{4,6}
Order-7 square tiling
4
7
{4,7}
Order-8 square tiling
4
8
{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
4.10
2
t{5,4}
Truncated pentahexagonal tiling
4.10.12
tr{6,5}
Truncated order-4 hexagonal tiling
4.12
2
t{6,4}
Truncated hexaoctagonal tiling
4.12.16
tr{8,6}
Truncated order-4 heptagonal tiling
4.14
2
t{7,4}
Truncated order-4 octagonal tiling
4.16
2
t{8,4}
Truncated order-4 apeirogonal tiling
4.∞
2
t{∞,4}
Tetraapeirogonal tiling
4.∞.4.∞
r{∞,4}
Order-4 pentagonal tiling
5
4
{5,4}
Order-5 pentagonal tiling
5
5
{5,5}
Order-6 pentagonal tiling
5
6
{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
5.8
2
t{4,5}
Truncated order-5 pentagonal tiling
5.10
2
t{5,5}
Truncated order-5 hexagonal tiling
5.12
2
t{6,5}
Pentaapeirogonal tiling
5.∞.5.∞
r{∞,5}
Order-4 hexagonal tiling
6
4
{6,4}
Order-5 hexagonal tiling
6
5
{6,5}
Order-6 hexagonal tiling
6
6
{6,6}
Order-8 hexagonal tiling
6
8
{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
6.8
2
t{4,6}
Truncated order-6 pentagonal tiling
6.10
2
t{5,6}
Truncated order-6 hexagonal tiling
6.12
2
t{6,6}
Truncated order-6 octagonal tiling
6.16
2
t{8,6}
Heptagonal tiling
7
3
{7,3}
Order-4 heptagonal tiling
7
4
{7,4}
Order-7 heptagonal tiling
7
7
{7,7}
Truncated order-7 triangular tiling
7.6
2
t{3,7}
Truncated order-7 square tiling
7.8
2
t{4,7}
Truncated order-7 heptagonal tiling
7.14
2
t{7,7}
Octagonal tiling
8
3
{8,3}
Order-4 octagonal tiling
8
4
{8,4}
Order-6 octagonal tiling
8
6
{8,6}
Order-8 octagonal tiling
8
8
{8,8}
Truncated order-8 hexagonal tiling
8
12
t{6,8}
Truncated order-8 triangular tiling
8.6
2
t{3,8}
Truncated order-8 octagonal tiling
8.16
2
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
∞.6
2
t{3,∞}
Truncated infinite-order square tiling
∞.8
2
t{4,∞}
See also
Uniform tiling
Convex uniform honeycombs
List of k-uniform tilings
List of Euclidean uniform tilings
Uniform tilings in hyperbolic plane
Tessellation
Periodic
Pythagorean
Rhombille
Schwarz triangle
Rectangle
Domino
Uniform tiling
and
honeycomb
Coloring
Convex
Kisrhombille
Wallpaper group
Wythoff
Aperiodic
Ammann–Beenker
Aperiodic set of prototiles
List
Einstein problem
Socolar–Taylor
Gilbert
Penrose
Pentagonal
Pinwheel
Quaquaversal
Rep-tile
and
Self-tiling
Sphinx
Socolar
Truchet
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
2
n
3
3
.n
V3
3
.n
4
2
.n
V4
2
.n
Regular
2
∞
3
6
4
4
6
3
Semi-
regular
3
2
.4.3.4
V3
2
.4.3.4
3
3
.4
2
3
3
.∞
3
4
.6
V3
4
.6
3.4.6.4
(3.6)
2
3.12
2
4
2
.∞
4.6.12
4.8
2
Hyper-
bolic
3
2
.4.3.5
3
2
.4.3.6
3
2
.4.3.7
3
2
.4.3.8
3
2
.4.3.∞
3
2
.5.3.5
3
2
.5.3.6
3
2
.6.3.6
3
2
.6.3.8
3
2
.7.3.7
3
2
.8.3.8
3
3
.4.3.4
3
2
.∞.3.∞
3
4
.7
3
4
.8
3
4
.∞
3
5
.4
3
7
3
8
3
∞
(3.4)
3
(3.4)
4
3.4.6
2
.4
3.4.7.4
3.4.8.4
3.4.∞.4
3.6.4.6
(3.7)
2
(3.8)
2
3.14
2
3.16
2
(3.∞)
2
3.∞
2
4
2
.5.4
4
2
.6.4
4
2
.7.4
4
2
.8.4
4
2
.∞.4
4
5
4
6
4
7
4
8
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.∞
4.10
2
4.10.12
4.12
2
4.12.16
4.14
2
4.16
2
4.∞
2
(4.∞)
2
5
4
5
5
5
6
5
∞
5.4.6.4
(5.6)
2
5.8
2
5.10
2
5.12
2
(5.∞)
2
6
4
6
5
6
6
6
8
6.4.8.4
(6.8)
2
6.8
2
6.10
2
6.12
2
6.16
2
7
3
7
4
7
7
7.6
2
7.8
2
7.14
2
8
3
8
4
8
6
8
8
8.6
2
8.12
2
8.16
2
∞
3
∞
4
∞
5
∞
∞
∞.6
2
∞.8
2
This article is issued from
Wikipedia
. The text is licensed under
Creative Commons - Attribution - Sharealike
. Additional terms may apply for the media files.
