# Hexagonal lattice Two-dimensional Bravais lattices:
1 – oblique (monoclinic),
2 – rectangular (orthorhombic),
3 – centered rectangular (orthorhombic),
4hexagonal,
5 – square (tetragonal).

The hexagonal lattice or triangular lattice is one of the five two-dimensional Bravais lattice types. The symmetry category of the lattice is wallpaper group p6m. The primitive translation vectors of the hexagonal lattice form an angle of 120° and are of equal lengths,

$|\mathbf {a} _{1}|=|\mathbf {a} _{2}|=a$ .

The reciprocal lattice of the hexagonal lattice is a hexagonal lattice in reciprocal space with orientation changed by 90° and primitive lattice vectors of length

$g={\frac {4\pi }{a{\sqrt {3}}}}$ .

## Honeycomb lattice Honeycomb lattice as a hexagonal lattice with a two-atom basis. The gray rhombus is a primitive cell. Vectors $\mathbf {a} _{1}$ and $\mathbf {a} _{2}$ are primitive translation vectors.

The honeycomb lattice is a special case of the hexagonal lattice with a two-atom basis. The centers of the hexagons of a honeycomb form a hexagonal lattice, and the honeycomb lattice can be seen as the union of two offset triangular lattices.

In nature, carbon atoms of the two-dimensional material graphene are arranged in a honeycomb lattice.