Hexagonal tiling
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| Hexagonal tiling | |
|---|---|
 |
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| Type | Regular tiling |
| Faces | hexagons |
| Edges | Infinite |
| Vertices | Infinite |
| Vertex configuration | 6.6.6 |
| Wythoff symbol | 3 | 2 6 |
| Symmetry group | p6m |
| Dual | Triangular tiling |
| Properties | planar, vertex-uniform |
 Vertex Figure |
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In geometry, the hexagonal tiling is a regular tiling of the Euclidean plane. It has Schläfli symbol of t0{6,3} or t2{3,6}.
The internal angle of the hexagon is 120 degrees so three hexagons at a point make a full 360 degrees. It is one of three regular tilings of the plane. The other two are the square tiling and the triangular tiling.
This hexagonal pattern exists in nature in a beehive's honeycomb.
There are 3 distinct vertex-uniform colorings of a hexagonal tiling. (Naming the colors by indices on the 3 hexagons around a vertex: 111, 112, 123.)
This tiling is topologically related as a part of sequence of regular polyhedra with vertex figure (n3).
 (33) |
 (43) |
 (53) |
 (63) tiling |
It is also topologically related as a part of sequence of uniform truncated polyhedra with vertex figure (n.6.6).
 (3.6.6) |
 (4.6.6) |
 (5.6.6) |
 (6.6.6) tiling |
See also:
- hexagonal lattice
- Tilings of regular polygons
- List of uniform planar tilings
- List of regular polytopes
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