The first Brillouin zone of a (simple) hexagonal lattice

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  Symmetry points  (u,v,w)  [kx,ky,kz]  Point group    
  Γ: (0,0,0)    [0,0,0]

6/mmm

  A: (0,0,1/2)    [0,0,π/c]  

6/mmm

  K: (2/3,1/3,0)    [4π/3a,0,0]  

62m

  H: (2/3,1/3,1/2)    [4π/3a,0,π/c]  

62m

  M: (1/2,0,0)    [π/a,-π/√3a,0]  

mmm

  L: (1/2,0,1/2)    [π/a,-π/√3a,π/c]  

mmm

  Symmetry lines    Point group  
  Δ: (0,0,w)  0 < w < 1/2  

6mm

  P: (2/3,1/3,w)  0 < w < 1/2  

3m

  U: (1/2,0,w)  0 < w < 1/2  

mm2

  Λ: (2v,v,0)  0 < v < 1/3  

mm2

  Q: (2v,v,1/2)  0 < v < 1/3  

mm2

  Σ: (u,0,0)  0 < u < 1/2  

mm2

  R: (u,0,1/2)  0 < u < 1/2  

mm2

  T: (1/2+v/2,v,0)  0 < v < 1/3  

mm2

  S: (1/2+v/2,v,1/2)  0 < v < 1/3  

mm2

The real space and reciprocal space primitive translation vectors are:

The first Brillouin zone of an hexagonal lattice is hexagonal again. Some crystals with an (simple) hexagonal Bravais lattice are Mg, Nd, Sc, Ti, Zn, Be, Cd, Ce, Y.