Home > The 17 wallpaper groups > Hexagonal lattice

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The 120 degrees rhombic cell - 3- and 6-fold rotations, with mirrors in three of the five groups.

The hexagonal lattice carries 3-fold and 6-fold rotations. p3 and p6 are rotation-only; p3m1, p31m, and p6m add mirrors - and p3m1 vs p31m differ only in where the mirrors sit relative to the 3-fold centers.

Each group is shown as three figures - the tiling view (the motif repeated, with the fundamental-domain tile tinted and the V1/V2 cell vectors marked), the group's cluster node, and the symmetry-elements view in international notation. See the overview for how to read them, and Reading the symmetry notation for what the codes mean.

p3 - 3-fold rotations only

p3m1 - every 3-fold on a mirror line

p31m - mirrors along the cell edges; some 3-folds off them

p6 - 6-, 3-, and 2-fold rotations, no mirrors

p6m - full 6-fold symmetry, mirrors in all six directions

< Previous: Square lattice | Next: Reading the symmetry notation >

• The 17 wallpaper groups: the overview and the other lattices.
• Reading the symmetry notation: how to read the group codes.