# Orthorhombic crystal system

In crystallography, the orthorhombic crystal system is one of the 7 crystal systems. Orthorhombic lattices result from stretching a cubic lattice along two of its orthogonal pairs by two different factors, resulting in a rectangular prism with a rectangular base (a by b) and height (c), such that a, b, and c are distinct. All three bases intersect at 90° angles, so the three lattice vectors remain mutually orthogonal.

## Bravais lattices

Rectangular vs rhombic unit cells for the 2D orthorhombic lattices. The swapping of centering type when the unit cell is changed also applies for the 3D orthorhombic lattices

### Two-dimensional

In two dimensions there are two orthorhombic Bravais lattices: primitive rectangular and centered rectangular. 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.

### Three-dimensional

In three dimensions, there are four orthorhombic Bravais lattices: primitive orthorhombic, base-centered orthorhombic, body-centered orthorhombic, and face-centered orthorhombic.

Bravais lattice Primitive
orthorhombic
Base-centered
orthorhombic
Body-centered
orthorhombic
Face-centered
orthorhombic
Pearson symbol oP oS oI oF
Standard unit cell
Right rhombic prism
unit cell

In the orthorhombic system there is a rarely used second choice of crystal axes that results in a unit cell with the shape of a right rhombic prism;[1] it can be constructed because the rectangular two-dimensional base layer can also be described with rhombic axes. In this axis setting, the primitive and base-centered lattices swap in centering type, while the same thing happens with the body-centered and face-centered lattices. Note that the length ${\displaystyle a}$ in the lower row is not the same as in the upper row, as can be seen in the figure in the section on two-dimensional lattices. For the first and third column above, ${\displaystyle a}$ of the second row equals ${\displaystyle {\sqrt {a^{2}+b^{2}}}}$ of the first row, and for the second and fourth column it equals half of this.