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The square cell - 4-fold rotations, with or without mirrors.

The square lattice carries 4-fold (quarter-turn) rotations. p4 has rotations only; p4m sets the 4-folds on mirror lines; p4g puts diagonal mirrors and axial glides with the 4-folds off the mirrors.

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.

p4 - 4-fold and 2-fold rotations, no mirrors

p4m - 4-folds sitting on mirror lines

p4g - 4-folds off the mirrors; diagonal mirrors, axial glides

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