Orthorhombic crystal system

<h2 id="bravais-lattices">Bravais lattices</h2>
<p class="note">Further information: <a href="/facts/Bravais_lattice/7gQKTsXk">Bravais lattice</a></p>
<p>There are four orthorhombic Bravais lattices: primitive orthorhombic, base-centered orthorhombic, body-centered orthorhombic, and face-centered orthorhombic.
</p>
<table><tbody><tr><th>Bravais lattice</th><th>Primitiveorthorhombic</th><th>Base-centeredorthorhombic</th><th>Body-centeredorthorhombic</th><th>Face-centeredorthorhombic</th></tr><tr><th><a href="/facts/Pearson_symbol/K3qljnNu">Pearson symbol</a></th><td>oP</td><td>oS</td><td>oI</td><td>oF</td></tr><tr><th><a href="/facts/Unit_cell/znygJqdx">Unit cell</a></th><td></td><td></td><td></td><td></td></tr></tbody></table>
<p>For the base-centered orthorhombic lattice, the <a href="/facts/Primitive_cell/znygJqdx">primitive cell</a> has the shape of a right rhombic prism;<a class="footnote-ref" id="fnref:1" href="#fn:1"><sup>1</sup></a> it can be constructed because the two-dimensional centered rectangular base layer can also be described with primitive rhombic axes. Note that the length 
  
    
      
        a
      
    
    {\displaystyle a}
  
 of the primitive cell below equals 
  
    
      
        
          
            1
            2
          
        
        
          
            
              a
              
                2
              
            
            +
            
              b
              
                2
              
            
          
        
      
    
    {\displaystyle {\frac {1}{2}}{\sqrt {a^{2}+b^{2}}}}
  
 of the conventional cell above.
</p>
Right rhombic prism primitive cellPrimitive cell of the base-centered orthorhombic latticeRelationship between base layers of primitive and conventional cells
<h2 id="crystal-classes">Crystal classes</h2>
<p class="note">Further information: <a href="/facts/Crystallographic_point_group/43NqYrf0">Crystallographic point group</a></p>
<p>The <i>orthorhombic crystal system</i> class names, examples, <a href="/facts/Sch%25C3%25B6nflies_notation/c4y0GtEt">Schönflies notation</a>, <a href="/facts/Hermann-Mauguin_notation/NGHDFXKC">Hermann-Mauguin notation</a>, point groups, International Tables for Crystallography space group number,<a class="footnote-ref" id="fnref:2" href="#fn:2"><sup>2</sup></a> <a href="/facts/Orbifold_notation/HCbBoa2J">orbifold notation</a>, type, and <a href="/facts/Space_group/2XQx0J7M">space groups</a> are listed in the table below.
</p>
<table><tbody><tr><th rowspan="2"><a href="/facts/Space_group/2XQx0J7M">№</a></th><th colspan="5">Point group</th><th rowspan="2">Type</th><th rowspan="2">Example</th><th colspan="4"><a href="/facts/Space_group/2XQx0J7M">Space groups</a></th></tr><tr><th>Name<a class="footnote-ref" id="fnref:3" href="#fn:3"><sup>3</sup></a></th><th><a href="/facts/Schoenflies_notation/c4y0GtEt">Schön.</a></th><th><a href="/facts/Hermann-Mauguin_notation/NGHDFXKC">Intl</a></th><th><a href="/facts/Orbifold_notation/HCbBoa2J">Orb.</a></th><th><a href="/facts/Coxeter_notation/ArUw6goe">Cox.</a> </th><th>Primitive</th><th>Base-centered</th><th>Face-centered</th><th>Body-centered</th></tr><tr><th>16–24</th><td>Rhombic disphenoidal</td><td>D2 (V)</td><td>222</td><td>222</td><td>[2,2]+</td><td><a href="/facts/Enantiomorphic/p5a9pftB">Enantiomorphic</a></td><td><a href="/facts/Epsomite/kNs2K16I">Epsomite</a><p><a href="/facts/Boron/Pmwgd7Mf">Boron</a>(gamma form)</p></td><td>P222, P2221, P21212, P212121</td><td>C2221, C222</td><td>F222</td><td>I222, I212121</td></tr><tr><th>25–46</th><td>Rhombic pyramidal</td><td>C2v</td><td>mm2</td><td>*22</td><td>[2]</td><td><a href="/facts/Polar_point_group/2aeoGxhc">Polar</a></td><td><a href="/facts/Hemimorphite/YDXNAQDb">Hemimorphite</a>, <a href="/facts/Bertrandite/RKJvfCDC">bertrandite</a></td><td>Pmm2, Pmc21, Pcc2, Pma2, Pca21, Pnc2, Pmn21, Pba2, Pna21, Pnn2</td><td>Cmm2, Cmc21, Ccc2Amm2, Aem2, Ama2, Aea2</td><td>Fmm2, Fdd2</td><td>Imm2, Iba2, Ima2</td></tr><tr><th>47–74</th><td>Rhombic dipyramidal</td><td>D2h (Vh)</td><td>mmm</td><td>*222</td><td>[2,2]</td><td><a href="/facts/Centrosymmetric/nIFJqujU">Centrosymmetric</a></td><td><a href="/facts/Olivine/tLLL4rae">Olivine</a>, <a href="/facts/Aragonite/QGcD3SLs">aragonite</a>, <a href="/facts/Marcasite/vP4CW3QC">marcasite</a></td><td>Pmmm, Pnnn, Pccm, Pban, Pmma, Pnna, Pmna, Pcca, Pbam, Pccn, Pbcm, Pnnm, Pmmn, Pbcn, Pbca, Pnma</td><td>Cmcm, Cmce, Cmmm, Cccm, Cmme, Ccce</td><td>Fmmm, Fddd</td><td>Immm, Ibam, Ibca, Imma</td></tr></tbody></table>
<h2 id="in-two-dimensions">In two dimensions</h2>
<p class="note">Main article: <a href="/facts/Rectangular_lattice/2ls9Iv9N">Rectangular lattice</a></p>
<p>In two dimensions there are two orthorhombic Bravais lattices: primitive rectangular and centered rectangular.
</p>
<table><tbody><tr><th>Bravais lattice</th><th>Rectangular</th><th>Centered rectangular</th></tr><tr><th><a href="/facts/Pearson_symbol/K3qljnNu">Pearson symbol</a></th><td>op</td><td>oc</td></tr><tr><th><a href="/facts/Unit_cell/znygJqdx">Unit cell</a></th><td></td><td></td></tr></tbody></table>
<h2 id="see-also">See also</h2>
<ul><li><a href="/facts/Crystal_structure/bJ4bCeHd">Crystal structure</a></li>
<li><a href="/facts/Crystal_system/dMQLk1q4">Crystal system</a></li>
<li><a href="/facts/List_of_the_230_crystallographic_3D_space_groups/2XQx0J7M">Overview of all space groups</a></li></ul>

<h2 id="further-reading">Further reading</h2>
<ul><li>Hurlbut, Cornelius S.; Klein, Cornelis (1985). <a href="https://archive.org/details/manualofmineralo00klei/page/69"><i>Manual of Mineralogy</i></a> (20th ed.). pp. <a href="https://archive.org/details/manualofmineralo00klei/page/69">69–73</a>. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-471-80580-7.</li>
<li>Hahn, Theo, ed. (2002). <a href="http://it.iucr.org/A/"><i>International Tables for Crystallography, Volume A: Space Group Symmetry</i></a>. International Tables for Crystallography. Vol. A (5th ed.). Berlin, New York: <a href="/facts/Springer-Verlag/nAesf6nT">Springer-Verlag</a>. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1107%2F97809553602060000100">10.1107/97809553602060000100</a>. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-7923-6590-7.</li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>See Hahn (2002), p. 746, row oC, column Primitive, where the cell parameters are given as a1 = a2, α = β = 90° - Hahn, Theo, ed. (2002). International Tables for Crystallography, Volume A: Space Group Symmetry. International Tables for Crystallography. Vol. A (5th ed.). Berlin, New York: Springer-Verlag. doi:10.1107/97809553602060000100. ISBN 978-0-7923-6590-7. <a href="http://it.iucr.org/A/" target="_blank">http://it.iucr.org/A/</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>Prince, E., ed. (2006). International Tables for Crystallography. International Union of Crystallography. doi:10.1107/97809553602060000001. ISBN 978-1-4020-4969-9. S2CID 146060934. <a href="978-1-4020-4969-9" target="_blank">978-1-4020-4969-9</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
<li id="fn:3"><p>"The 32 crystal classes". Retrieved 2018-06-19. <a href="https://www.tulane.edu/~sanelson/eens211/32crystalclass.htm" target="_blank">https://www.tulane.edu/~sanelson/eens211/32crystalclass.htm</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li>
</ol>

Orthorhombic crystal system open-in-new

Orthorhombic crystal system