Hexagonal lattice	Wallpaper group p6m	Unit cell

Thehexagonal lattice (sometimes calledtriangular lattice) is one of the five two-dimensionalBravais lattice types.^[1] Thesymmetry category of the lattice iswallpaper group p6m.^[2] The primitive translation vectors of the hexagonal lattice form an angle of 120° and are of equal lengths,

${\displaystyle |{\mathbf{a}}_1|=|{\mathbf{a}}_2|=a.}$

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

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

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 materialgraphene are arranged in a honeycomb point set.

Thehexagonal lattice class names,Schönflies notation,Hermann-Mauguin notation,orbifold notation,Coxeter notation, andwallpaper groups are listed in the table below.

• Square lattice (see dots in a diagonal square centered)
• Hexagonal tiling
• Close-packing
• Centered hexagonal number
• Eisenstein integer
• Voronoi diagram
• Hermite constant

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• Lattice points
• Crystal systems

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