Home > The 17 wallpaper groups > Rectangular lattice

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Rectangular and rhombic cells - mirror and glide lines running along the edges.

The rectangular lattice adds reflections. Mirror and/or glide lines run along the cell edges, with pmg and pgg also carrying half-turns. Its centered (rhombic) variant - the cm/cmm groups - is included below.

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.

pm - parallel mirror lines

pg - parallel glide lines

pmm - two perpendicular mirror families

pmg - mirrors one way, glides + 2-folds the other

pgg - perpendicular glides + 2-folds, no mirrors

The centered-rectangular (rhombic) lattice is the rectangular family's variant: an extra lattice point at the cell center, easiest to describe on a rhombus. Its two groups alternate mirror and glide lines.

cm - alternating mirror and glide lines

cmm - perpendicular mirrors + 2-folds on and off the mirrors

< Previous: Oblique lattice | Next: Square lattice >

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