Hexagonal latticeWallpaper group p6mUnit cell
The hexagonal lattice (sometimes called 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,
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
Honeycomb point set
The honeycomb point set 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 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.
Crystal classes The hexagonal lattice class names, Schönflies notation, Hermann-Mauguin notation, orbifold notation, Coxeter notation, and wallpaper groups are listed in the table below. Geometric class, point groupWallpaper groupsSchön. Intl Orb. Cox. C33(33)+ p3(333) D33m(*33) p3m1(*333) p31m(3*3) C66(66)+ p6(632) D66mm(*66) p6m(*632)
See also Square lattice (see dots in a diagonal square centered) Hexagonal tiling Close-packing Centered hexagonal number Eisenstein integer Voronoi diagram Hermite constant
References