# 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

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
Unit cell

For the base-centered orthorhombic lattice, the primitive cell has the shape of a right rhombic prism;[1] it can be constructed because the two-dimensional centered rectangular base layer can also be described with primitive rhombic axes. Note that the length ${\displaystyle a}$ of the primitive cell below equals ${\displaystyle {\frac {1}{2}}{\sqrt {a^{2}+b^{2}}}}$ of the conventional cell above.

Right rhombic prism primitive cell
Primitive cell of the base-centered orthorhombic lattice
Relationship between base layers of primitive and conventional cells

## Crystal classes

The orthorhombic crystal system class names, examples, Schönflies notation, Hermann-Mauguin notation, point groups, International Tables for Crystallography space group number,[2] orbifold notation, type, and space groups are listed in the table below.

Point group Type Example Space groups
Name[3] Schön. Intl Orb. Cox.  Primitive Base-centered Face-centered Body-centered
16–24 Rhombic disphenoidal D2 (V) 222 222 [2,2]+ Enantiomorphic Epsomite P222, P2221, P21212, P212121 C2221, C222 F222 I222, I212121
25–46 Rhombic pyramidal C2v mm2 *22 [2] Polar Hemimorphite, bertrandite Pmm2, Pmc21, Pcc2, Pma2, Pca21, Pnc2, Pmn21, Pba2, Pna21, Pnn2 Cmm2, Cmc21, Ccc2
Amm2, Aem2, Ama2, Aea2
Fmm2, Fdd2 Imm2, Iba2, Ima2
47–74 Rhombic dipyramidal D2h (Vh) mmm *222 [2,2] Centrosymmetric Olivine, aragonite, marcasite Pmmm, Pnnn, Pccm, Pban, Pmma, Pnna, Pmna, Pcca, Pbam, Pccn, Pbcm, Pnnm, Pmmn, Pbcn, Pbca, Pnma Cmcm, Cmca, Cmmm, Cccm, Cmme, Ccce Fmmm, Fddd Immm, Ibam, Ibca, Imma

## In two dimensions

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

Bravais lattice Rectangular Centered rectangular
Pearson symbol op oc
Unit cell