https://wiki.uni-konstanz.de/ccp4/index.php?title=Resolution&feed=atom&action=history Resolution - Revision history 2024-03-28T14:45:45Z Revision history for this page on the wiki MediaWiki 1.39.6 https://wiki.uni-konstanz.de/ccp4/index.php?title=Resolution&diff=2799&oldid=prev Kay: fix typo 2022-12-07T07:56:19Z <p>fix typo</p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 08:56, 7 December 2022</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The resolution of a reflection &lt;math&gt;(hkl)&lt;/math&gt; is defined as the inverse of the reciprocal lattice vector, i.e. &lt;math&gt;\frac{1}{r^2} = \mathbf{d}^{*} \cdot \mathbf{d}^{*}&lt;/math&gt; with &lt;math&gt; \mathbf{d}^{*} = h \mathbf{a}^{*} + k \mathbf{b}^{*} + l \mathbf{c}^{*}&lt;/math&gt;.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The resolution of a reflection &lt;math&gt;(hkl)&lt;/math&gt; is defined as the inverse of the reciprocal lattice vector, i.e. &lt;math&gt;\frac{1}{r^2} = \mathbf{d}^{*} \cdot \mathbf{d}^{*}&lt;/math&gt; with &lt;math&gt; \mathbf{d}^{*} = h \mathbf{a}^{*} + k \mathbf{b}^{*} + l \mathbf{c}^{*}&lt;/math&gt;.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The formula to calculate the resolution from the unit cell dimensions &lt;math&gt;a, b, c, \alpha, \beta, \gamma&lt;/math&gt; looks a little <del style="font-weight: bold; text-decoration: none;">appaling</del>:</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The formula to calculate the resolution from the unit cell dimensions &lt;math&gt;a, b, c, \alpha, \beta, \gamma&lt;/math&gt; looks a little <ins style="font-weight: bold; text-decoration: none;">appalling</ins>:</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;math&gt;\frac{1}{r^2} = \frac{1}{\sin^2\beta - \sin^2\alpha} \left( \frac{l}{c} - \frac{k\cos \alpha}{b} - \frac{h\cos \beta}{a}\right)^2 + \left( \frac{ak-bh\cos\gamma}{ab\sin\gamma}\right)^2 + \frac{h^2}{a^2}&lt;/math&gt;.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;math&gt;\frac{1}{r^2} = \frac{1}{\sin^2\beta - \sin^2\alpha} \left( \frac{l}{c} - \frac{k\cos \alpha}{b} - \frac{h\cos \beta}{a}\right)^2 + \left( \frac{ak-bh\cos\gamma}{ab\sin\gamma}\right)^2 + \frac{h^2}{a^2}&lt;/math&gt;.</div></td></tr> </table> Kay https://wiki.uni-konstanz.de/ccp4/index.php?title=Resolution&diff=2798&oldid=prev Kay: the = was missing 2022-12-07T07:26:23Z <p>the = was missing</p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 08:26, 7 December 2022</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l3">Line 3:</td> <td colspan="2" class="diff-lineno">Line 3:</td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The formula to calculate the resolution from the unit cell dimensions &lt;math&gt;a, b, c, \alpha, \beta, \gamma&lt;/math&gt; looks a little appaling:</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The formula to calculate the resolution from the unit cell dimensions &lt;math&gt;a, b, c, \alpha, \beta, \gamma&lt;/math&gt; looks a little appaling:</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&lt;math&gt;\frac{1}{r^2} \frac{1}{\sin^2\beta - \sin^2\alpha} \left( \frac{l}{c} - \frac{k\cos \alpha}{b} - \frac{h\cos \beta}{a}\right)^2 + \left( \frac{ak-bh\cos\gamma}{ab\sin\gamma}\right)^2 + \frac{h^2}{a^2}&lt;/math&gt;.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&lt;math&gt;\frac{1}{r^2} <ins style="font-weight: bold; text-decoration: none;">= </ins>\frac{1}{\sin^2\beta - \sin^2\alpha} \left( \frac{l}{c} - \frac{k\cos \alpha}{b} - \frac{h\cos \beta}{a}\right)^2 + \left( \frac{ak-bh\cos\gamma}{ab\sin\gamma}\right)^2 + \frac{h^2}{a^2}&lt;/math&gt;.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>When the [[spacegroup]] is orthorombic, however, this formula simplifies to</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>When the [[spacegroup]] is orthorombic, however, this formula simplifies to</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;math&gt; \frac{1}{r^2} = \frac{h^2}{a^2} + \frac{k^2}{b^2} + \frac{l^2}{c^2}&lt;/math&gt;.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;math&gt; \frac{1}{r^2} = \frac{h^2}{a^2} + \frac{k^2}{b^2} + \frac{l^2}{c^2}&lt;/math&gt;.</div></td></tr> <!-- diff cache key ccp4:diff::1.12:old-1623:rev-2798 --> </table> Kay https://wiki.uni-konstanz.de/ccp4/index.php?title=Resolution&diff=1623&oldid=prev Grunet: fixed typos in math formulae 2010-02-28T10:13:43Z <p>fixed typos in math formulae</p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 11:13, 28 February 2010</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>The resolution of a reflection &lt;math&gt;(hkl)&lt;/math&gt; is defined as the inverse of the reciprocal lattice vector, i.e. &lt;math&gt;<del style="font-weight: bold; text-decoration: none;">r = \sqrt{</del>\frac{1}{\mathbf{d}^{*} \cdot <del style="font-weight: bold; text-decoration: none;">&lt;</del>mathbf{d}^{*<del style="font-weight: bold; text-decoration: none;">}}</del>}&lt;/math&gt; with &lt;math&gt; \mathbf{d}^{*} = h \<del style="font-weight: bold; text-decoration: none;">mathb</del>{a}^{*} + k {b}^{*} + l \<del style="font-weight: bold; text-decoration: none;">mathb</del>{c}^{*}&lt;/math&gt;.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>The resolution of a reflection &lt;math&gt;(hkl)&lt;/math&gt; is defined as the inverse of the reciprocal lattice vector, i.e. &lt;math&gt;\frac{1}{<ins style="font-weight: bold; text-decoration: none;">r^2} = </ins>\mathbf{d}^{*} \cdot <ins style="font-weight: bold; text-decoration: none;">\</ins>mathbf{d}^{*}&lt;/math&gt; with &lt;math&gt; \mathbf{d}^{*} = h \<ins style="font-weight: bold; text-decoration: none;">mathbf</ins>{a}^{*} + k <ins style="font-weight: bold; text-decoration: none;">\mathbf</ins>{b}^{*} + l \<ins style="font-weight: bold; text-decoration: none;">mathbf</ins>{c}^{*}&lt;/math&gt;.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The formula to calculate the resolution from the unit cell dimensions &lt;math&gt;a, b, c, \alpha, \beta, \gamma&lt;/math&gt; looks a little appaling:</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The formula to calculate the resolution from the unit cell dimensions &lt;math&gt;a, b, c, \alpha, \beta, \gamma&lt;/math&gt; looks a little appaling:</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>&lt;math&gt;\frac{1}{\sin^2\beta - \sin^2\alpha} \left( \frac{l}{c} - \frac{k\cos \alpha}{b} - \frac{h\cos \beta}{a}\right)^2 + \left( \frac{ak-bh\cos\gamma}{ab\sin\gamma}\right)^2 + \frac{h^2}{a^2}&lt;/math&gt;.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>&lt;math&gt;<ins style="font-weight: bold; text-decoration: none;">\frac{1}{r^2} </ins>\frac{1}{\sin^2\beta - \sin^2\alpha} \left( \frac{l}{c} - \frac{k\cos \alpha}{b} - \frac{h\cos \beta}{a}\right)^2 + \left( \frac{ak-bh\cos\gamma}{ab\sin\gamma}\right)^2 + \frac{h^2}{a^2}&lt;/math&gt;.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>When the [[spacegroup]] is orthorombic, however, this formula simplifies to</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>When the [[spacegroup]] is orthorombic, however, this formula simplifies to</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;math&gt; \frac{1}{r^2} = \frac{h^2}{a^2} + \frac{k^2}{b^2} + \frac{l^2}{c^2}&lt;/math&gt;.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>&lt;math&gt; \frac{1}{r^2} = \frac{h^2}{a^2} + \frac{k^2}{b^2} + \frac{l^2}{c^2}&lt;/math&gt;.</div></td></tr> </table> Grunet https://wiki.uni-konstanz.de/ccp4/index.php?title=Resolution&diff=1622&oldid=prev Grunet: /* Headline text */ 2010-02-27T15:18:32Z <p><span dir="auto"><span class="autocomment">Headline text</span></span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 16:18, 27 February 2010</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">== Headline text ==</del></div></td><td colspan="2" class="diff-side-added"></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The resolution of a reflection &lt;math&gt;(hkl)&lt;/math&gt; is defined as the inverse of the reciprocal lattice vector, i.e. &lt;math&gt;r = \sqrt{\frac{1}{\mathbf{d}^{*} \cdot &lt;mathbf{d}^{*}}}&lt;/math&gt; with &lt;math&gt; \mathbf{d}^{*} = h \mathb{a}^{*} + k {b}^{*} + l \mathb{c}^{*}&lt;/math&gt;.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The resolution of a reflection &lt;math&gt;(hkl)&lt;/math&gt; is defined as the inverse of the reciprocal lattice vector, i.e. &lt;math&gt;r = \sqrt{\frac{1}{\mathbf{d}^{*} \cdot &lt;mathbf{d}^{*}}}&lt;/math&gt; with &lt;math&gt; \mathbf{d}^{*} = h \mathb{a}^{*} + k {b}^{*} + l \mathb{c}^{*}&lt;/math&gt;.</div></td></tr> <tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr> </table> Grunet https://wiki.uni-konstanz.de/ccp4/index.php?title=Resolution&diff=1621&oldid=prev Grunet: Created this page because I couldn't find this formula on the web. 2010-02-27T15:18:14Z <p>Created this page because I couldn&#039;t find this formula on the web.</p> <p><b>New page</b></p><div>== Headline text ==<br /> The resolution of a reflection &lt;math&gt;(hkl)&lt;/math&gt; is defined as the inverse of the reciprocal lattice vector, i.e. &lt;math&gt;r = \sqrt{\frac{1}{\mathbf{d}^{*} \cdot &lt;mathbf{d}^{*}}}&lt;/math&gt; with &lt;math&gt; \mathbf{d}^{*} = h \mathb{a}^{*} + k {b}^{*} + l \mathb{c}^{*}&lt;/math&gt;.<br /> <br /> The formula to calculate the resolution from the unit cell dimensions &lt;math&gt;a, b, c, \alpha, \beta, \gamma&lt;/math&gt; looks a little appaling:<br /> <br /> &lt;math&gt;\frac{1}{\sin^2\beta - \sin^2\alpha} \left( \frac{l}{c} - \frac{k\cos \alpha}{b} - \frac{h\cos \beta}{a}\right)^2 + \left( \frac{ak-bh\cos\gamma}{ab\sin\gamma}\right)^2 + \frac{h^2}{a^2}&lt;/math&gt;.<br /> <br /> When the [[spacegroup]] is orthorombic, however, this formula simplifies to<br /> &lt;math&gt; \frac{1}{r^2} = \frac{h^2}{a^2} + \frac{k^2}{b^2} + \frac{l^2}{c^2}&lt;/math&gt;.</div> Grunet