Infinite-order hexagonal tiling | |
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![]() Poincaré disk model of the hyperbolic plane | |
Type | Hyperbolic regular tiling |
Vertex configuration | 6∞ |
Schläfli symbol | {6,∞} |
Wythoff symbol | ∞ | 6 2 |
Coxeter diagram | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Symmetry group | [∞,6], (*∞62) |
Dual | Order-6 apeirogonal tiling |
Properties | Vertex-transitive, edge-transitive, face-transitive |
In 2-dimensional hyperbolic geometry, the infinite-order hexagonal tiling is a regular tiling. It has Schläfli symbol of {6,∞}. All vertices are ideal, located at "infinity", seen on the boundary of the Poincaré hyperbolic disk projection.
There is a half symmetry form, , seen with alternating colors:
This tiling is topologically related as a part of sequence of regular polyhedra and tilings with vertex figure (6n).
*n62 symmetry mutation of regular tilings: {6,n} | ||||||||
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Spherical | Euclidean | Hyperbolic tilings | ||||||
![]() {6,2} |
![]() {6,3} |
![]() {6,4} |
![]() {6,5} |
![]() {6,6} |
![]() {6,7} |
![]() {6,8} |
... | ![]() {6,∞} |