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# 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.

Bravais lattice Rectangular Centered rectangular
Pearson symbol op oc
Standard unit cell
Rhombic unit cell

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 ${\displaystyle a}$ in the lower row is not the same as in the upper row. For the first column above, ${\displaystyle a}$ of the second row equals ${\displaystyle {\sqrt {a^{2}+b^{2}}}}$ of the first row, and for the second column it equals half of this.

### 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.

## 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