Hexagonal tiling

The hexagonal tiling, or hexat, is one of the three regular tilings of the Euclidean plane. 3 hexagons join at each vertex of this tiling. It can also be formed as a truncation of the triangular tiling.

Vertex coordinates
Coordinates for the vertices of a hexagonal tiling of edge length 1 are given by:


 * $$\left(3i\pm\frac12,\,\sqrt3j+\frac{\sqrt3}{2}\right),$$
 * $$\left(3i\pm1,\,\sqrt3j\right),$$

where i and j range over the integers.

Representations
A hexagonal tiling has the following Coxeter diagrams:


 * x6o3o (full symmetry)
 * o6x3x (as truncated triangular tiling)
 * x3x3x3*a ((P3 symmetry, as omnitruncated cyclotriangular tiling)
 * s6x3x (additional alternated faceting form)
 * x∞s2s∞o (as alternated faceting from the square tiling)
 * uBxx3uxBx3uxxB&#zx (B = 4)
 * ho3oo3oh&#zx (hull of two opposite triangular tilings)

In vertex figures
The hexagonal tiling appears as the vertex figure of the hyperbolic triangular tiling honeycomb.