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Tetragonal crystal system
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<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 two tetragonal Bravais lattices: the primitive tetragonal and the body-centered tetragonal. </p> <table><tbody><tr><th>Bravais lattice</th><th>Primitivetetragonal</th><th>Body-centeredtetragonal</th></tr><tr><th><a href="/facts/Pearson_symbol/K3qljnNu">Pearson symbol</a></th><td>tP</td><td>tI</td></tr><tr><th><a href="/facts/Unit_cell/znygJqdx">Unit cell</a></th><td></td><td></td></tr></tbody></table> <p>The body-centered tetragonal lattice is equivalent to the primitive tetragonal lattice with a smaller unit cell, while the face-centered tetragonal lattice is equivalent to the body-centered tetragonal lattice with a smaller unit cell.<a class="footnote-ref" id="fnref:1" href="#fn:1"><sup>1</sup></a> </p> <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 point groups that fall under this crystal system are listed below, followed by their representations in international notation, <a href="/facts/Schoenflies_notation/c4y0GtEt">Schoenflies notation</a>, <a href="/facts/Orbifold_notation/HCbBoa2J">orbifold notation</a>, <a href="/facts/Coxeter_notation/ArUw6goe">Coxeter notation</a> and <a href="/facts/Mineral/LkUFbNmv">mineral</a> examples.<a class="footnote-ref" id="fnref:2" href="#fn:2"><sup>2</sup></a><a class="footnote-ref" id="fnref:3" href="#fn:3"><sup>3</sup></a> </p> <table><tbody><tr><th rowspan="2">#</th><th colspan="5">Point group</th><th rowspan="2">Type</th><th rowspan="2">Example</th><th colspan="2"><a href="/facts/Space_group/2XQx0J7M">Space groups</a></th></tr><tr><th>Name<a class="footnote-ref" id="fnref:4" href="#fn:4"><sup>4</sup></a></th><th><a href="/facts/Hermann%25E2%2580%2593Mauguin_notation/NGHDFXKC">Intl</a></th><th><a href="/facts/Schoenflies_notation/c4y0GtEt">Schoen.</a></th><th><a href="/facts/Orbifold/KR6dQNzH">Orb.</a></th><th><a href="/facts/Coxeter_notation/ArUw6goe">Cox.</a></th><th>Primitive</th><th>Body-centered</th></tr><tr><th>75–80</th><td>Tetragonal pyramidal</td><td>4</td><td><i>C</i>4</td><td>44</td><td>[4]+</td><td><a href="/facts/Enantiomorphic/p5a9pftB">enantiomorphic</a> <a href="/facts/Polar_point_group/2aeoGxhc">polar</a></td><td><a href="/facts/Pinnoite/d0WgrJqD">pinnoite</a>, <a href="/facts/Piypite/JCLCCyLD">piypite</a></td><td>P4, P41, P42, P43</td><td>I4, I41</td></tr><tr><th>81–82</th><td>Tetragonal disphenoidal</td><td>4</td><td><i>S</i>4</td><td>2×</td><td>[2+,4+]</td><td></td><td><a href="/facts/Cahnite/G5qdEu4e">cahnite</a>, <a href="/facts/Tugtupite/uTsM6GsY">tugtupite</a></td><td>P4</td><td>I4</td></tr><tr><th>83–88</th><td>Tetragonal dipyramidal</td><td>4/m</td><td><i>C</i>4<i>h</i></td><td>4*</td><td>[2,4+]</td><td><a href="/facts/Centrosymmetric/nIFJqujU">centrosymmetric</a></td><td><a href="/facts/Scheelite/Te4N0qKN">scheelite</a>, <a href="/facts/Wulfenite/VFGdIlXF">wulfenite</a>, <a href="/facts/Leucite/l1uVJHtm">leucite</a></td><td>P4/m, P42/m, P4/n, P42/n</td><td>I4/m, I41/a</td></tr><tr><th>89–98</th><td>Tetragonal trapezohedral</td><td>422</td><td><i>D</i>4</td><td>224</td><td>[2,4]+</td><td><a href="/facts/Enantiomorphic/p5a9pftB">enantiomorphic</a></td><td><a href="/facts/Cristobalite/r1rQss4r">cristobalite</a>, <a href="/facts/Wardite/9Dn4E1E0">wardite</a></td><td>P422, P4212, P4122, P41212, P4222, P42212, P4322, P43212</td><td>I422, I4122</td></tr><tr><th>99–110</th><td>Ditetragonal pyramidal</td><td>4mm</td><td><i>C</i>4<i>v</i></td><td>*44</td><td>[4]</td><td><a href="/facts/Polar_point_group/2aeoGxhc">polar</a></td><td><a href="/facts/Diaboleite/Ug0pxaKr">diaboleite</a></td><td>P4mm, P4bm, P42cm, P42nm, P4cc, P4nc, P42mc, P42bc</td><td>I4mm, I4cm, I41md, I41cd</td></tr><tr><th>111–122</th><td>Tetragonal scalenohedral</td><td>42m</td><td><i>D</i>2<i>d</i> (Vd)</td><td>2*2</td><td>[2+,4]</td><td></td><td><a href="/facts/Chalcopyrite/MXBDffGw">chalcopyrite</a>, <a href="/facts/Stannite/omKID2Cy">stannite</a></td><td>P42m, P42c, P421m, P421c, P4m2, P4c2, P4b2, P4n2</td><td>I4m2, I4c2, I42m, I42d</td></tr><tr><th>123–142</th><td>Ditetragonal dipyramidal</td><td>4/mmm</td><td><i>D</i>4<i>h</i></td><td>*224</td><td>[2,4]</td><td><a href="/facts/Centrosymmetric/nIFJqujU">centrosymmetric</a></td><td><a href="/facts/Rutile/qwJH5ElN">rutile</a>, <a href="/facts/Pyrolusite/dnS0c7NK">pyrolusite</a>, <a href="/facts/Zircon/84APfbLt">zircon</a></td><td>P4/mmm, P4/mcc, P4/nbm, P4/nnc, P4/mbm, P4/mnc, P4/nmm, P4/ncc, P42/mmc, P42/mcm, P42/nbc, P42/nnm, P42/mbc, P42/mnm, P42/nmc, P42/ncm</td><td>I4/mmm, I4/mcm, I41/amd, I41/acd</td></tr></tbody></table> <h2 id="in-two-dimensions">In two dimensions</h2> <p class="note">Main article: <a href="/facts/Square_lattice/mcVtpcQK">Square lattice</a></p> <p>There is only one tetragonal <a href="/facts/Bravais_lattice/7gQKTsXk">Bravais lattice</a> in two dimensions: the square lattice. </p> <table><tbody><tr><th>Bravais lattice</th><th>Square</th></tr><tr><th><a href="/facts/Pearson_symbol/K3qljnNu">Pearson symbol</a></th><td>tp</td></tr><tr><th><a href="/facts/Unit_cell/znygJqdx">Unit cell</a></th><td></td></tr></tbody></table> <h2 id="see-also">See also</h2> <ul><li><a href="/facts/Bravais_lattices/7gQKTsXk">Bravais lattices</a></li> <li><a href="/facts/Crystal_system/dMQLk1q4">Crystal system</a></li> <li><a href="/facts/Crystal_structure/bJ4bCeHd">Crystal structure</a></li> <li><a href="/facts/Point_groups/41NSqUN6">Point groups</a></li></ul> <h2 id="external-links">External links</h2> <ul><li> Media related to Tetragonal lattices at Wikimedia Commons</li></ul> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>Cubic-to-Tetragonal Transition <a href="http://www.aem.umn.edu/people/faculty/shield/hane/tet.html" target="_blank">http://www.aem.umn.edu/people/faculty/shield/hane/tet.html</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>Webmineral data <a href="http://webmineral.com/crystal/Tetragonal.shtml" target="_blank">http://webmineral.com/crystal/Tetragonal.shtml</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> <li id="fn:3"><p>Hurlbut, Cornelius S.; Klein, Cornelis, 1985, Manual of Mineralogy, 20th ed., pp. 73–78, ISBN 0-471-80580-7 <a href="/wiki/ISBN_(identifier)" target="_blank">/wiki/ISBN_(identifier)</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li> <li id="fn:4"><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:4" class="footnote-back-ref">↩</a></p></li> </ol>