Order-7 heptagonal tiling | |
---|---|
![]() Poincaré disk model of the hyperbolic plane | |
Type | Hyperbolic regular tiling |
Vertex configuration | 77 |
Schläfli symbol | {7,7} |
Wythoff symbol | 7 | 7 2 |
Coxeter diagram | ![]() ![]() ![]() ![]() ![]() |
Symmetry group | [7,7], (*772) |
Dual | self dual |
Properties | Vertex-transitive, edge-transitive, face-transitive |
In geometry, the order-7 heptagonal tiling is a regular tiling of the hyperbolic plane. It has Schläfli symbol of {7,7}, constructed from seven heptagons around every vertex. As such, it is self-dual.
Uniform heptaheptagonal tilings | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Symmetry: [7,7], (*772) | [7,7]+, (772) | ||||||||||
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() = ![]() ![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() = ![]() ![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() = ![]() ![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() = ![]() ![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() = ![]() ![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() = ![]() ![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() = ![]() ![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() = ![]() ![]() ![]() ![]() ![]() | ||||
![]() |
![]() |
![]() |
![]() |
![]() |
![]() |
![]() |
![]() | ||||
{7,7} |
t{7,7} |
r{7,7} | 2t{7,7}=t{7,7} | 2r{7,7}={7,7} | rr{7,7} | tr{7,7} | sr{7,7} | ||||
Uniform duals | |||||||||||
![]() ![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() ![]() | ||||
![]() |
![]() |
![]() |
![]() |
![]() |
![]() |
![]() |
|||||
V77 | V7.14.14 | V7.7.7.7 | V7.14.14 | V77 | V4.7.4.7 | V4.14.14 | V3.3.7.3.7 |
This tiling is a part of regular series {n,7}:
Tiles of the form {n,7} | ||||||||
---|---|---|---|---|---|---|---|---|
Spherical | Hyperbolic tilings | |||||||
![]() {2,7} ![]() ![]() ![]() ![]() ![]() |
![]() {3,7} ![]() ![]() ![]() ![]() ![]() |
![]() {4,7} ![]() ![]() ![]() ![]() ![]() |
![]() {5,7} ![]() ![]() ![]() ![]() ![]() |
![]() {6,7} ![]() ![]() ![]() ![]() ![]() |
![]() {7,7} ![]() ![]() ![]() ![]() ![]() |
![]() {8,7} ![]() ![]() ![]() ![]() ![]() |
... |
![]() {∞,7} ![]() ![]() ![]() ![]() ![]() |
Order-7 heptagonal tiling | |
---|---|
![]() Poincaré disk model of the hyperbolic plane | |
Type | Hyperbolic regular tiling |
Vertex configuration | 77 |
Schläfli symbol | {7,7} |
Wythoff symbol | 7 | 7 2 |
Coxeter diagram | ![]() ![]() ![]() ![]() ![]() |
Symmetry group | [7,7], (*772) |
Dual | self dual |
Properties | Vertex-transitive, edge-transitive, face-transitive |
In geometry, the order-7 heptagonal tiling is a regular tiling of the hyperbolic plane. It has Schläfli symbol of {7,7}, constructed from seven heptagons around every vertex. As such, it is self-dual.
Uniform heptaheptagonal tilings | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Symmetry: [7,7], (*772) | [7,7]+, (772) | ||||||||||
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() = ![]() ![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() = ![]() ![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() = ![]() ![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() = ![]() ![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() = ![]() ![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() = ![]() ![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() = ![]() ![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() = ![]() ![]() ![]() ![]() ![]() | ||||
![]() |
![]() |
![]() |
![]() |
![]() |
![]() |
![]() |
![]() | ||||
{7,7} |
t{7,7} |
r{7,7} | 2t{7,7}=t{7,7} | 2r{7,7}={7,7} | rr{7,7} | tr{7,7} | sr{7,7} | ||||
Uniform duals | |||||||||||
![]() ![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() ![]() |
![]() ![]() ![]() ![]() ![]() | ||||
![]() |
![]() |
![]() |
![]() |
![]() |
![]() |
![]() |
|||||
V77 | V7.14.14 | V7.7.7.7 | V7.14.14 | V77 | V4.7.4.7 | V4.14.14 | V3.3.7.3.7 |
This tiling is a part of regular series {n,7}:
Tiles of the form {n,7} | ||||||||
---|---|---|---|---|---|---|---|---|
Spherical | Hyperbolic tilings | |||||||
![]() {2,7} ![]() ![]() ![]() ![]() ![]() |
![]() {3,7} ![]() ![]() ![]() ![]() ![]() |
![]() {4,7} ![]() ![]() ![]() ![]() ![]() |
![]() {5,7} ![]() ![]() ![]() ![]() ![]() |
![]() {6,7} ![]() ![]() ![]() ![]() ![]() |
![]() {7,7} ![]() ![]() ![]() ![]() ![]() |
![]() {8,7} ![]() ![]() ![]() ![]() ![]() |
... |
![]() {∞,7} ![]() ![]() ![]() ![]() ![]() |