Infinite-order hexagonal tiling
From Infogalactic: the planetary knowledge core
{{{Ui6_2-name}}} | |
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[[image:{{{Ui6_2-image}}}|280px|Infinite-order hexagonal tiling]] Poincaré disk model of the hyperbolic plane |
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Type | Hyperbolic regular tiling |
Vertex figure | {{{Ui6_2-vfig}}} |
Schläfli symbol | {{{Ui6_2-schl}}} |
Wythoff symbol | {{{Ui6_2-Wythoff}}} |
Coxeter diagram | {{{Ui6_2-CD}}} |
Symmetry group | {{{Ui6_2-group}}} |
Dual | [[{{{Ui6_2-dual}}}]] |
Properties | Vertex-transitive, edge-transitive, face-transitive {{{Ui6_2-special}}} |
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.
Symmetry
There is a half symmetry form, , seen with alternating colors:
Related polyhedra and tiling
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,∞} |
See also
Wikimedia Commons has media related to Infinite-order pentagonal tiling. |
References
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