Hexagonal lattice

[1] 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, 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 The honeycomb point set is a special case of the hexagonal lattice with a two-atom basis.

[1] The centers of the hexagons of a honeycomb form a hexagonal lattice, and the honeycomb point set can be seen as the union of two offset hexagonal lattices.

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

The hexagonal lattice class names, Schönflies notation, Hermann-Mauguin notation, orbifold notation, Coxeter notation, and wallpaper groups are listed in the table below.

Honeycomb point set as a hexagonal lattice with a two-atom basis. The gray rhombus is a primitive cell. Vectors and are primitive translation vectors.