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Source: Hexagonal lattice

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,

|

a

1

|

=

|

a

2

|

=
a
.

{\displaystyle |\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
=

4
π

a

3

.

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