| 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,∞}
|
|
|
