Rectangular lattice

The rectangular lattice and centered rectangular lattice (or rhombic 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 (or 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

{\displaystyle a}

in the lower row is not the same as in the upper row. For the first column above,

a

{\displaystyle a}

of the second row equals

a

2

+

b

2

{\displaystyle {\sqrt {a^{2}+b^{2}}}}

of the first row, and for the second column it equals

1

2

a

2

+

b

2

{\displaystyle {\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.