Rectangular lattice

The rectangular lattice and rhombic lattice (or centered rectangular lattice) constitute two of the five two-dimensional Bravais lattice types. The symmetry categories of these lattices are wallpaper groups pmm and cmm respectively. The conventional translation vectors of the rectangular lattices form an angle of 90° and are of unequal lengths.

Bravais lattices
There are two rectangular Bravais lattices: primitive rectangular and centered rectangular (also rhombic).



The primitive rectangular lattice can also be described by a centered rhombic unit cell, while the centered rectangular lattice can also be described by a primitive rhombic unit cell. Note that the length $$a$$ in the lower row is not the same as in the upper row. For the first column above, $$a$$ of the second row equals $$\sqrt{a^2+b^2}$$ of the first row, and for the second column it equals $$\frac{1}{2} \sqrt{a^2+b^2}$$.

Crystal classes
The rectangular lattice class names, Schönflies notation, Hermann-Mauguin notation, orbifold notation, Coxeter notation, and wallpaper groups are listed in the table below.