https://dictionary.iucr.org/index.php?title=Lattice_complex&feed=atom&action=history
Lattice complex - Revision history
2024-03-29T13:49:51Z
Revision history for this page on the wiki
MediaWiki 1.30.0
https://dictionary.iucr.org/index.php?title=Lattice_complex&diff=4509&oldid=prev
BrianMcMahon: Tidied translations.
2017-11-14T17:51:47Z
<p>Tidied translations.</p>
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<td colspan="2" style="background-color: white; color:black; text-align: center;">Revision as of 17:51, 14 November 2017</td>
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<tr><td class='diff-marker'>−</td><td style="color:black; 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 class="diffchange diffchange-inline">Font </del>color="red"> Gittercomplex</<del class="diffchange diffchange-inline">Font</del>> (''Ge'').</div></td><td class='diff-marker'>+</td><td style="color:black; 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><<ins class="diffchange diffchange-inline">font </ins>color="red">Gittercomplex</<ins class="diffchange diffchange-inline">font</ins>> (''Ge'').</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
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BrianMcMahon
https://dictionary.iucr.org/index.php?title=Lattice_complex&diff=4026&oldid=prev
BrianMcMahon: Style edits to align with printed edition
2017-05-15T14:45:34Z
<p>Style edits to align with printed edition</p>
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<td colspan="2" style="background-color: white; color:black; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: white; color:black; text-align: center;">Revision as of 14:45, 15 May 2017</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l6" >Line 6:</td>
<td colspan="2" class="diff-lineno">Line 6:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>A ''lattice complex'' is the set of all [[point configuration]]s that may be generated within one type of [[Wyckoff set]]. All [[Wyckoff position]]s, Wyckoff sets and types of Wyckoff sets that generate the same set of point configurations are assigned to the same lattice complex.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>A ''lattice complex'' is the set of all [[point configuration]]s that may be generated within one type of [[Wyckoff set]]. All [[Wyckoff position]]s, Wyckoff sets and types of Wyckoff sets that generate the same set of point configurations are assigned to the same lattice complex.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; 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>Concretely, two Wyckoff positions are assigned to the same lattice complex if there is a suitable transformation that maps the point configurations of the two Wyckoff positions onto each other and if their space groups belong to the same [[crystal family]]. The 72 (in E<sup>2</sup>) or 1731 (in E<sup>3</sup>) Wyckoff positions are classified in 51 (E<sup>2</sup>) or 1128 (E<sup>3</sup>) types of Wyckoff sets. They are assigned to 30 (E<sup>2</sup>) or 402 (E<sup>3</sup>) lattice complexes.</div></td><td class='diff-marker'>+</td><td style="color:black; 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>Concretely, two Wyckoff positions are assigned to the same lattice complex if there is a suitable transformation that maps the point configurations of the two Wyckoff positions onto each other and if their space groups belong to the same [[crystal family]]. The 72 (in <ins class="diffchange diffchange-inline">''</ins>E<ins class="diffchange diffchange-inline">''</ins><sup>2</sup>) or 1731 (in <ins class="diffchange diffchange-inline">''</ins>E<ins class="diffchange diffchange-inline">''</ins><sup>3</sup>) Wyckoff positions are classified in 51 (<ins class="diffchange diffchange-inline">''</ins>E<ins class="diffchange diffchange-inline">''</ins><sup>2</sup>) or 1128 (<ins class="diffchange diffchange-inline">''</ins>E<ins class="diffchange diffchange-inline">''</ins><sup>3</sup>) types of Wyckoff sets. They are assigned to 30 (<ins class="diffchange diffchange-inline">''</ins>E<ins class="diffchange diffchange-inline">''</ins><sup>2</sup>) or 402 (<ins class="diffchange diffchange-inline">''</ins>E<ins class="diffchange diffchange-inline">''</ins><sup>3</sup>) lattice complexes.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The name ''lattice complex'' comes from the fact that an assemblage of points that are equivalent with respect to a group of symmetry operations including lattice translations can be visualized as a set of equivalent lattices.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The name ''lattice complex'' comes from the fact that an assemblage of points that are equivalent with respect to a group of symmetry operations including lattice translations can be visualized as a set of equivalent lattices.</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l27" >Line 27:</td>
<td colspan="2" class="diff-lineno">Line 27:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><tr><td>B</td><td>000, <math>\frac{1}{2}</math>0<math>\frac{1}{2}</math></td><td>2</td></tr></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><tr><td>B</td><td>000, <math>\frac{1}{2}</math>0<math>\frac{1}{2}</math></td><td>2</td></tr></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><tr><td>C</td><td>000, <math>\frac{1}{2}</math><math>\frac{1}{2}</math>0</td><td>2</td></tr></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><tr><td>C</td><td>000, <math>\frac{1}{2}</math><math>\frac{1}{2}</math>0</td><td>2</td></tr></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; 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><tr><td>D (Diamond structure)</td><td>000<del class="diffchange diffchange-inline">. </del><math>\frac{1}{4}</math><math>\frac{1}{4}</math><math>\frac{1}{4}</math>, 0<math>\frac{1}{2}</math><math>\frac{1}{2}</math>, <math>\frac{1}{2}</math>0,<math>\frac{1}{2}</math>, <math>\frac{1}{2}</math><math>\frac{1}{2}</math>0,<br><math>\frac{3}{4}</math><math>\frac{3}{4}</math><math>\frac{1}{4}</math>, <math>\frac{3}{4}</math><math>\frac{1}{4}</math><math>\frac{3}{4}</math>, <math>\frac{1}{4}</math><math>\frac{3}{4}</math><math>\frac{3}{4}</math></td><td>8</td></tr></div></td><td class='diff-marker'>+</td><td style="color:black; 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><tr><td>D (Diamond structure)</td><td>000<ins class="diffchange diffchange-inline">, </ins><math>\frac{1}{4}</math><math>\frac{1}{4}</math><math>\frac{1}{4}</math>, 0<math>\frac{1}{2}</math><math>\frac{1}{2}</math>, <math>\frac{1}{2}</math>0,<math>\frac{1}{2}</math>, <math>\frac{1}{2}</math><math>\frac{1}{2}</math>0,<br><math>\frac{3}{4}</math><math>\frac{3}{4}</math><math>\frac{1}{4}</math>, <math>\frac{3}{4}</math><math>\frac{1}{4}</math><math>\frac{3}{4}</math>, <math>\frac{1}{4}</math><math>\frac{3}{4}</math><math>\frac{3}{4}</math></td><td>8</td></tr></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><tr><td>E (Hexagonal close packing; Italian: Esagonale)</td><td><math>\frac{1}{3}</math><math>\frac{2}{3}</math><math>\frac{1}{4}</math>, <math>\frac{2}{3}</math><math>\frac{1}{3}</math><math>\frac{3}{4}</math></td><td>2</td></tr></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><tr><td>E (Hexagonal close packing; Italian: Esagonale)</td><td><math>\frac{1}{3}</math><math>\frac{2}{3}</math><math>\frac{1}{4}</math>, <math>\frac{2}{3}</math><math>\frac{1}{3}</math><math>\frac{3}{4}</math></td><td>2</td></tr></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><tr><td>F</td><td>000, 0<math>\frac{1}{2}</math><math>\frac{1}{2}</math>, <math>\frac{1}{2}</math>0<math>\frac{1}{2}</math>, <math>\frac{1}{2}</math><math>\frac{1}{2}</math>0</td><td>4</td></tr></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><tr><td>F</td><td>000, 0<math>\frac{1}{2}</math><math>\frac{1}{2}</math>, <math>\frac{1}{2}</math>0<math>\frac{1}{2}</math>, <math>\frac{1}{2}</math><math>\frac{1}{2}</math>0</td><td>4</td></tr></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><tr><td>G (Graphene)</td><td><math>\frac{1}{3}</math><math>\frac{2}{3}</math>0, <math>\frac{2}{3}</math><math>\frac{1}{3}</math>0 (hexagonal cell)</td><td>2</td></tr></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><tr><td>G (Graphene)</td><td><math>\frac{1}{3}</math><math>\frac{2}{3}</math>0, <math>\frac{2}{3}</math><math>\frac{1}{3}</math>0 (hexagonal cell)</td><td>2</td></tr></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><tr><td>I </td><td>000, <math>\frac{1}{2}</math><math>\frac{1}{2}</math><math>\frac{1}{2}</math></td><td>2</td></tr></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><tr><td>I </td><td>000, <math>\frac{1}{2}</math><math>\frac{1}{2}</math><math>\frac{1}{2}</math></td><td>2</td></tr></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; 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><tr><td>J (<del class="diffchange diffchange-inline">"</del>Jack<del class="diffchange diffchange-inline">"</del>)</td><td>0<math>\frac{1}{2}</math><math>\frac{1}{2}</math>, <math>\frac{1}{2}</math>0<math>\frac{1}{2}</math>, <math>\frac{1}{2}</math><math>\frac{1}{2}</math>0</td><td>3</td></tr></div></td><td class='diff-marker'>+</td><td style="color:black; 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><tr><td>J (<ins class="diffchange diffchange-inline">'</ins>Jack<ins class="diffchange diffchange-inline">'</ins>)</td><td>0<math>\frac{1}{2}</math><math>\frac{1}{2}</math>, <math>\frac{1}{2}</math>0<math>\frac{1}{2}</math>, <math>\frac{1}{2}</math><math>\frac{1}{2}</math>0</td><td>3</td></tr></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; 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><tr><td>J* = J+<math>\frac{1}{2}</math><math>\frac{1}{2}</math><math>\frac{1}{2}</math>J</td><td>0<math>\frac{1}{2}</math><math>\frac{1}{2}</math>, <math>\frac{1}{2}</math>0<math>\frac{1}{2}</math>, <math>\frac{1}{2}</math><math>\frac{1}{2}</math>0<br><math>\frac{1}{2}</math>00, 0<math>\frac{1}{2}</math>0, 00<math>\frac{1}{2}</math></td><td>6</td></tr></div></td><td class='diff-marker'>+</td><td style="color:black; 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><tr><td>J* = J+<math>\frac{1}{2}</math><math>\frac{1}{2}</math><math>\frac{1}{2}</math>J</td><td>0<math>\frac{1}{2}</math><math>\frac{1}{2}</math>, <math>\frac{1}{2}</math>0<math>\frac{1}{2}</math>, <math>\frac{1}{2}</math><math>\frac{1}{2}</math>0<ins class="diffchange diffchange-inline">,</ins><br><math>\frac{1}{2}</math>00, 0<math>\frac{1}{2}</math>0, 00<math>\frac{1}{2}</math></td><td>6</td></tr></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><tr><td>M</td><td>J in rhombohedral cell</td><td>3</td></tr></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><tr><td>M</td><td>J in rhombohedral cell</td><td>3</td></tr></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; 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><tr><td>N (Kagome <del class="diffchange diffchange-inline">Net</del>)</td><td><math>\frac{1}{2}</math>00, 0<math>\frac{1}{2}</math>0, <math>\frac{1}{2}</math><math>\frac{1}{2}</math>0 (hexagonal cell)</td><td>2</td></tr></div></td><td class='diff-marker'>+</td><td style="color:black; 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><tr><td>N (Kagome <ins class="diffchange diffchange-inline">net</ins>)</td><td><math>\frac{1}{2}</math>00, 0<math>\frac{1}{2}</math>0, <math>\frac{1}{2}</math><math>\frac{1}{2}</math>0 (hexagonal cell)</td><td>2</td></tr></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><tr><td>P</td><td>000</td><td>1</td></tr></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><tr><td>P</td><td>000</td><td>1</td></tr></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><tr><td><sup>+</sup>Q</td><td><math>\frac{1}{2}</math>00, 0<math>\frac{1}{2}</math><math>\frac{2}{3}</math>, <math>\frac{1}{2}</math><math>\frac{1}{2}</math><math>\frac{1}{3}</math> (hexagonal cell)</td><td>3</td></tr></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><tr><td><sup>+</sup>Q</td><td><math>\frac{1}{2}</math>00, 0<math>\frac{1}{2}</math><math>\frac{2}{3}</math>, <math>\frac{1}{2}</math><math>\frac{1}{2}</math><math>\frac{1}{3}</math> (hexagonal cell)</td><td>3</td></tr></div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l60" >Line 60:</td>
<td colspan="2" class="diff-lineno">Line 60:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== Symbols of variant lattice complexes ==</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== Symbols of variant lattice complexes ==</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; 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 symbol of a lattice complex with degrees of freedom may contain up to four <del class="diffchange diffchange-inline">pats</del>:</div></td><td class='diff-marker'>+</td><td style="color:black; 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 symbol of a lattice complex with degrees of freedom may contain up to four <ins class="diffchange diffchange-inline">parts</ins>:</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>* a shift vector;</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>* a shift vector;</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>* the distribution symmetry;</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>* the distribution symmetry;</div></td></tr>
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<td colspan="2" class="diff-lineno">Line 71:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== See also ==</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== See also ==</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; 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>*Chapter 3.4 of <del class="diffchange diffchange-inline">[http://it.iucr.org/A/ </del>''International Tables <del class="diffchange diffchange-inline">of </del>Crystallography, <del class="diffchange diffchange-inline">Section </del>A'', <del class="diffchange diffchange-inline">6<sup>th</sup> </del>edition<del class="diffchange diffchange-inline">]<br></del></div></td><td class='diff-marker'>+</td><td style="color:black; 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>*Chapter 3.4 of ''International Tables <ins class="diffchange diffchange-inline">for </ins>Crystallography, <ins class="diffchange diffchange-inline">Volume </ins>A'', <ins class="diffchange diffchange-inline">6th </ins>edition</div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; 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> </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>[[Category:Fundamental crystallography]]</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>[[Category:Fundamental crystallography]]</div></td></tr>
</table>
BrianMcMahon
https://dictionary.iucr.org/index.php?title=Lattice_complex&diff=3851&oldid=prev
MassimoNespolo: /* See also */ 6th edition of ITA
2017-04-10T16:01:21Z
<p><span dir="auto"><span class="autocomment">See also: </span> 6th edition of ITA</span></p>
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<td colspan="2" style="background-color: white; color:black; text-align: center;">Revision as of 16:01, 10 April 2017</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== See also ==</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== See also ==</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; 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> </div></td><td class='diff-marker'>+</td><td style="color:black; 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><ins class="diffchange diffchange-inline">*</ins>Chapter <ins class="diffchange diffchange-inline">3.4 </ins>of [http://it.iucr.org/A/ ''International Tables of Crystallography, Section A''<ins class="diffchange diffchange-inline">, 6<sup>th</sup> edition</ins>]<br></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; 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>Chapter <del class="diffchange diffchange-inline">14 </del>of [http://it.iucr.org/A/ ''International Tables of Crystallography, Section A'']<br></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; 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> </div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>[[Category:Fundamental crystallography]]</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>[[Category:Fundamental crystallography]]</div></td></tr>
</table>
MassimoNespolo
https://dictionary.iucr.org/index.php?title=Lattice_complex&diff=3452&oldid=prev
MassimoNespolo: typo
2015-01-26T09:49:52Z
<p>typo</p>
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<td colspan="2" style="background-color: white; color:black; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: white; color:black; text-align: center;">Revision as of 09:49, 26 January 2015</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l6" >Line 6:</td>
<td colspan="2" class="diff-lineno">Line 6:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>A ''lattice complex'' is the set of all [[point configuration]]s that may be generated within one type of [[Wyckoff set]]. All [[Wyckoff position]]s, Wyckoff sets and types of Wyckoff sets that generate the same set of point configurations are assigned to the same lattice complex.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>A ''lattice complex'' is the set of all [[point configuration]]s that may be generated within one type of [[Wyckoff set]]. All [[Wyckoff position]]s, Wyckoff sets and types of Wyckoff sets that generate the same set of point configurations are assigned to the same lattice complex.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; 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>Concretely, two Wyckoff positions are assigned to the same lattice complex if there is a suitable <del class="diffchange diffchange-inline">trasformation </del>that maps the point configurations of the two Wyckoff positions onto each other and if their space groups belong to the same [[crystal family]]. The 72 (in E<sup>2</sup>) or 1731 (in E<sup>3</sup>) Wyckoff positions are classified in 51 (E<sup>2</sup>) or 1128 (E<sup>3</sup>) types of Wyckoff sets. They are assigned to 30 (E<sup>2</sup>) or 402 (E<sup>3</sup>) lattice complexes.</div></td><td class='diff-marker'>+</td><td style="color:black; 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>Concretely, two Wyckoff positions are assigned to the same lattice complex if there is a suitable <ins class="diffchange diffchange-inline">transformation </ins>that maps the point configurations of the two Wyckoff positions onto each other and if their space groups belong to the same [[crystal family]]. The 72 (in E<sup>2</sup>) or 1731 (in E<sup>3</sup>) Wyckoff positions are classified in 51 (E<sup>2</sup>) or 1128 (E<sup>3</sup>) types of Wyckoff sets. They are assigned to 30 (E<sup>2</sup>) or 402 (E<sup>3</sup>) lattice complexes.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The name ''lattice complex'' comes from the fact that an assemblage of points that are equivalent with respect to a group of symmetry operations including lattice translations can be visualized as a set of equivalent lattices.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The name ''lattice complex'' comes from the fact that an assemblage of points that are equivalent with respect to a group of symmetry operations including lattice translations can be visualized as a set of equivalent lattices.</div></td></tr>
</table>
MassimoNespolo
https://dictionary.iucr.org/index.php?title=Lattice_complex&diff=3387&oldid=prev
MassimoNespolo: /* Symbols of invariant lattice complexes */ a couple of typos spotted by Gervais
2014-07-15T07:38:02Z
<p><span dir="auto"><span class="autocomment">Symbols of invariant lattice complexes: </span> a couple of typos spotted by Gervais</span></p>
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<td colspan="2" style="background-color: white; color:black; text-align: center;">Revision as of 07:38, 15 July 2014</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l45" >Line 45:</td>
<td colspan="2" class="diff-lineno">Line 45:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><tr><td>T</td><td><math>\frac{1}{8}</math><math>\frac{1}{8}</math><math>\frac{1}{8}</math>, <math>\frac{3}{8}</math><math>\frac{3}{8}</math><math>\frac{1}{8}</math>, <math>\frac{1}{8}</math><math>\frac{5}{8}</math><math>\frac{5}{8}</math>, <math>\frac{7}{8}</math><math>\frac{7}{8}</math><math>\frac{1}{8}</math>, <math>\frac{7}{8}</math><math>\frac{5}{8}</math><math>\frac{3}{8}</math> + permutations</td><td>16</td></tr></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><tr><td>T</td><td><math>\frac{1}{8}</math><math>\frac{1}{8}</math><math>\frac{1}{8}</math>, <math>\frac{3}{8}</math><math>\frac{3}{8}</math><math>\frac{1}{8}</math>, <math>\frac{1}{8}</math><math>\frac{5}{8}</math><math>\frac{5}{8}</math>, <math>\frac{7}{8}</math><math>\frac{7}{8}</math><math>\frac{1}{8}</math>, <math>\frac{7}{8}</math><math>\frac{5}{8}</math><math>\frac{3}{8}</math> + permutations</td><td>16</td></tr></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><tr><td><sup>+</sup>V</td><td><math>\frac{1}{4}</math><math>\frac{1}{8}</math>0, <math>\frac{3}{4}</math><math>\frac{3}{8}</math>0, <math>\frac{3}{4}</math><math>\frac{5}{8}</math><math>\frac{1}{2}</math>, <math>\frac{7}{8}</math><math>\frac{1}{2}</math><math>\frac{1}{4}</math> + permutations</td><td>12</td></tr></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><tr><td><sup>+</sup>V</td><td><math>\frac{1}{4}</math><math>\frac{1}{8}</math>0, <math>\frac{3}{4}</math><math>\frac{3}{8}</math>0, <math>\frac{3}{4}</math><math>\frac{5}{8}</math><math>\frac{1}{2}</math>, <math>\frac{7}{8}</math><math>\frac{1}{2}</math><math>\frac{1}{4}</math> + permutations</td><td>12</td></tr></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; 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><tr><td><del class="diffchange diffchange-inline">'</del>V</td><td>V·-1</td><td>12</td></tr></div></td><td class='diff-marker'>+</td><td style="color:black; 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><tr><td><ins class="diffchange diffchange-inline"><sup>-</sup></ins>V</td><td<ins class="diffchange diffchange-inline">><sup>+</sup</ins>>V·-1</td><td>12</td></tr></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; 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><tr><td>V*</td><td>V + <del class="diffchange diffchange-inline">'</del>V</td><td>24</td></tr></div></td><td class='diff-marker'>+</td><td style="color:black; 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><tr><td>V*</td><td<ins class="diffchange diffchange-inline">><sup>+</sup</ins>>V + <ins class="diffchange diffchange-inline"><sup>-</sup></ins>V</td><td>24</td></tr></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><tr><td>W</td><td><math>\frac{1}{2}</math><math>\frac{1}{4}</math>0, 0<math>\frac{1}{2}</math><math>\frac{3}{4}</math> + permutations</td><td>6</td></tr></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><tr><td>W</td><td><math>\frac{1}{2}</math><math>\frac{1}{4}</math>0, 0<math>\frac{1}{2}</math><math>\frac{3}{4}</math> + permutations</td><td>6</td></tr></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><tr><td>W'</td><td><math>\frac{1}{2}</math><math>\frac{1}{2}</math><math>\frac{1}{2}</math>W</td><td>6</td></tr></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><tr><td>W'</td><td><math>\frac{1}{2}</math><math>\frac{1}{2}</math><math>\frac{1}{2}</math>W</td><td>6</td></tr></div></td></tr>
</table>
MassimoNespolo
https://dictionary.iucr.org/index.php?title=Lattice_complex&diff=3220&oldid=prev
BrianMcMahon: Fixed some broken HTML in the table.
2012-02-06T15:49:25Z
<p>Fixed some broken HTML in the table.</p>
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><tr><td><sup>-</sup>Y'</td><td><math>\frac{1}{2}</math><math>\frac{1}{2}</math><math>\frac{1}{2}</math><sup>-</sup>Y</td><td>4</td></tr></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><tr><td><sup>-</sup>Y'</td><td><math>\frac{1}{2}</math><math>\frac{1}{2}</math><math>\frac{1}{2}</math><sup>-</sup>Y</td><td>4</td></tr></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; 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><tr><td><sup>+</sup>Y*</td><td><sup>+</sup>Y+<sup>+</sup>Y'<td>8<del class="diffchange diffchange-inline"></td></del></td></tr></div></td><td class='diff-marker'>+</td><td style="color:black; 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><tr><td><sup>+</sup>Y*</td><td><sup>+</sup>Y+<sup>+</sup>Y'<td>8</td></tr></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; 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><tr><td><sup>-</sup>Y*</td><td><sup>-</sup>Y+<sup>-</sup>Y'<td>8<del class="diffchange diffchange-inline"></td></del></td></tr></div></td><td class='diff-marker'>+</td><td style="color:black; 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><tr><td><sup>-</sup>Y*</td><td><sup>-</sup>Y+<sup>-</sup>Y'<td>8</td></tr></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; 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><tr><td>Y**</td><td><sup>+</sup>Y*+<sup>-</sup>Y*<td>16<del class="diffchange diffchange-inline"></td></del></td></tr></div></td><td class='diff-marker'>+</td><td style="color:black; 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><tr><td>Y**</td><td><sup>+</sup>Y*+<sup>-</sup>Y*<td>16</td></tr></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div></table></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div></table></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
</table>
BrianMcMahon
https://dictionary.iucr.org/index.php?title=Lattice_complex&diff=2882&oldid=prev
MassimoNespolo: /* See also */ link
2009-02-13T15:25:34Z
<p><span dir="auto"><span class="autocomment">See also: </span> link</span></p>
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<td colspan="2" style="background-color: white; color:black; text-align: center;">Revision as of 15:25, 13 February 2009</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== See also ==</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== See also ==</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; 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>Chapter 14 of ''International Tables of Crystallography, Section A''<br></div></td><td class='diff-marker'>+</td><td style="color:black; 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>Chapter 14 of <ins class="diffchange diffchange-inline">[http://it.iucr.org/A/ </ins>''International Tables of Crystallography, Section A''<ins class="diffchange diffchange-inline">]</ins><br></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>[[Category:Fundamental crystallography]]</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>[[Category:Fundamental crystallography]]</div></td></tr>
</table>
MassimoNespolo
https://dictionary.iucr.org/index.php?title=Lattice_complex&diff=2881&oldid=prev
MassimoNespolo: /* Classification */ typo and rearrangement
2009-02-13T15:23:16Z
<p><span dir="auto"><span class="autocomment">Classification: </span> typo and rearrangement</span></p>
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>==Classification==</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>==Classification==</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; 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>If a <del class="diffchange diffchange-inline">first </del>lattice complex <del class="diffchange diffchange-inline">formes a true subset </del>of <del class="diffchange diffchange-inline">a second one, ''i''</del>.''<del class="diffchange diffchange-inline">e</del>''. <del class="diffchange diffchange-inline">if each </del>point configuration of the <del class="diffchange diffchange-inline">first </del>lattice complex <del class="diffchange diffchange-inline">also belongs to </del>the <del class="diffchange diffchange-inline">second one</del>, <del class="diffchange diffchange-inline">then </del>the <del class="diffchange diffchange-inline">first </del>one is called <del class="diffchange diffchange-inline">a '''limiting complex'</del>'' of the <del class="diffchange diffchange-inline">second one and the second complex is called a '''comprehensive </del>complex''<del class="diffchange diffchange-inline">' of the first one</del>.</div></td><td class='diff-marker'>+</td><td style="color:black; 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>If a lattice complex <ins class="diffchange diffchange-inline">can be generated in different space-group types, one </ins>of <ins class="diffchange diffchange-inline">them stands out because its corresponding [[Wyckoff position]]s show the highest [[site symmetry]]</ins>. <ins class="diffchange diffchange-inline">This is called the </ins>''<ins class="diffchange diffchange-inline">characteristic space-group type of the lattice complex</ins>''. <ins class="diffchange diffchange-inline">The characteristic space-group type and the corresponding oriented [[site symmetry]] express the common symmetry properties of all [[</ins>point configuration<ins class="diffchange diffchange-inline">]]s </ins>of <ins class="diffchange diffchange-inline">a lattice complex. In </ins>the <ins class="diffchange diffchange-inline">symbol of a </ins>lattice complex<ins class="diffchange diffchange-inline">, however, instead of </ins>the <ins class="diffchange diffchange-inline">[[site symmetry]]</ins>, the <ins class="diffchange diffchange-inline">Wyckoff letter of </ins>one <ins class="diffchange diffchange-inline">of the [[Wyckoff position]]s with that [[site symmetry]] is given. This [[Wyckoff position]] </ins>is called <ins class="diffchange diffchange-inline">the </ins>''<ins class="diffchange diffchange-inline">characteristic Wyckoff position </ins>of the <ins class="diffchange diffchange-inline">lattice </ins>complex''.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; 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>If a lattice complex <del class="diffchange diffchange-inline">can be generated in different space-group types</del>, <del class="diffchange diffchange-inline">one of them stands out because its corresponding [[Wyckoff position]]s show the highest [[site symmetry]]</del>. <del class="diffchange diffchange-inline">This is called the </del>''<del class="diffchange diffchange-inline">characteristic space-group type of the lattice complex</del>''. <del class="diffchange diffchange-inline">The characteristic space-group type and the corresponding oriented [[site symmetry]] express the common symmetry properties of all [[</del>point configuration<del class="diffchange diffchange-inline">]]s </del>of <del class="diffchange diffchange-inline">a </del>lattice complex<del class="diffchange diffchange-inline">. In </del>the <del class="diffchange diffchange-inline">symbol of </del>a <del class="diffchange diffchange-inline">lattice </del>complex<del class="diffchange diffchange-inline">, however, instead </del>of the <del class="diffchange diffchange-inline">[[site symmetry]], the Wyckoff letter of </del>one <del class="diffchange diffchange-inline">of </del>the <del class="diffchange diffchange-inline">[[Wyckoff position]]s with that [[site symmetry]] is given. This [[Wyckoff position]] </del>is called <del class="diffchange diffchange-inline">the </del>''<del class="diffchange diffchange-inline">characteristic Wyckoff position of the lattice </del>complex''.</div></td><td class='diff-marker'>+</td><td style="color:black; 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>If a <ins class="diffchange diffchange-inline">first </ins>lattice complex <ins class="diffchange diffchange-inline">forms a true subset of a second one</ins>, <ins class="diffchange diffchange-inline">''i''</ins>.''<ins class="diffchange diffchange-inline">e</ins>''. <ins class="diffchange diffchange-inline">if each </ins>point configuration of <ins class="diffchange diffchange-inline">the first </ins>lattice complex <ins class="diffchange diffchange-inline">also belongs to the second one, then </ins>the <ins class="diffchange diffchange-inline">first one is called </ins>a <ins class="diffchange diffchange-inline">'''limiting </ins>complex<ins class="diffchange diffchange-inline">''' </ins>of the <ins class="diffchange diffchange-inline">second </ins>one <ins class="diffchange diffchange-inline">and </ins>the <ins class="diffchange diffchange-inline">second complex </ins>is called <ins class="diffchange diffchange-inline">a '</ins>''<ins class="diffchange diffchange-inline">comprehensive </ins>complex''<ins class="diffchange diffchange-inline">' of the first one</ins>.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Lattice complexes are called ''invariant'' if they can occupy a parameterless position in a space group. The points in an invariant lattice complex can be split into different assemblages of equivalent points, the sum of which constitute a ''variant'' lattice complex (also termed a ''lattice complex with degrees of freedom''). Variant lattice complexes are classified into ''univariant'', ''bivariant'' and ''trivariant'' according to the number of parameters that can be varied independently.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Lattice complexes are called ''invariant'' if they can occupy a parameterless position in a space group. The points in an invariant lattice complex can be split into different assemblages of equivalent points, the sum of which constitute a ''variant'' lattice complex (also termed a ''lattice complex with degrees of freedom''). Variant lattice complexes are classified into ''univariant'', ''bivariant'' and ''trivariant'' according to the number of parameters that can be varied independently.</div></td></tr>
</table>
MassimoNespolo
https://dictionary.iucr.org/index.php?title=Lattice_complex&diff=2880&oldid=prev
MassimoNespolo: /* Definition */ new section : classification
2009-02-13T15:22:47Z
<p><span dir="auto"><span class="autocomment">Definition: </span> new section : classification</span></p>
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Concretely, two Wyckoff positions are assigned to the same lattice complex if there is a suitable trasformation that maps the point configurations of the two Wyckoff positions onto each other and if their space groups belong to the same [[crystal family]]. The 72 (in E<sup>2</sup>) or 1731 (in E<sup>3</sup>) Wyckoff positions are classified in 51 (E<sup>2</sup>) or 1128 (E<sup>3</sup>) types of Wyckoff sets. They are assigned to 30 (E<sup>2</sup>) or 402 (E<sup>3</sup>) lattice complexes.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>Concretely, two Wyckoff positions are assigned to the same lattice complex if there is a suitable trasformation that maps the point configurations of the two Wyckoff positions onto each other and if their space groups belong to the same [[crystal family]]. The 72 (in E<sup>2</sup>) or 1731 (in E<sup>3</sup>) Wyckoff positions are classified in 51 (E<sup>2</sup>) or 1128 (E<sup>3</sup>) types of Wyckoff sets. They are assigned to 30 (E<sup>2</sup>) or 402 (E<sup>3</sup>) lattice complexes.</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; 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;"></del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The name ''lattice complex'' comes from the fact that an assemblage of points that are equivalent with respect to a group of symmetry operations including lattice translations can be visualized as a set of equivalent lattices.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>The name ''lattice complex'' comes from the fact that an assemblage of points that are equivalent with respect to a group of symmetry operations including lattice translations can be visualized as a set of equivalent lattices.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; 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><ins style="font-weight: bold; text-decoration: none;">==Classification==</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>If a first lattice complex formes a true subset of a second one, ''i''.''e''. if each point configuration of the first lattice complex also belongs to the second one, then the first one is called a '''limiting complex''' of the second one and the second complex is called a '''comprehensive complex''' of the first one.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>If a first lattice complex formes a true subset of a second one, ''i''.''e''. if each point configuration of the first lattice complex also belongs to the second one, then the first one is called a '''limiting complex''' of the second one and the second complex is called a '''comprehensive complex''' of the first one.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
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MassimoNespolo
https://dictionary.iucr.org/index.php?title=Lattice_complex&diff=2879&oldid=prev
MassimoNespolo: /* Definition */ link
2009-02-13T15:21:14Z
<p><span dir="auto"><span class="autocomment">Definition: </span> link</span></p>
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<td colspan="2" style="background-color: white; color:black; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: white; color:black; text-align: center;">Revision as of 15:21, 13 February 2009</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>A ''lattice complex'' is the set of all [[point configuration]]s that may be generated within one type of [[Wyckoff set]]. All [[Wyckoff position]]s, Wyckoff sets and types of Wyckoff sets that generate the same set of point configurations are assigned to the same lattice complex.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>A ''lattice complex'' is the set of all [[point configuration]]s that may be generated within one type of [[Wyckoff set]]. All [[Wyckoff position]]s, Wyckoff sets and types of Wyckoff sets that generate the same set of point configurations are assigned to the same lattice complex.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; 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>Concretely, two Wyckoff positions are assigned to the same lattice complex if there is a suitable trasformation that maps the point configurations of the two Wyckoff positions onto each other and if their space groups belong to the same crystal family. The 72 (in E<sup>2</sup>) or 1731 (in E<sup>3</sup>) Wyckoff positions are classified in 51 (E<sup>2</sup>) or 1128 (E<sup>3</sup>) types of Wyckoff sets. They are assigned to 30 (E<sup>2</sup>) or 402 (E<sup>3</sup>) lattice complexes.</div></td><td class='diff-marker'>+</td><td style="color:black; 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>Concretely, two Wyckoff positions are assigned to the same lattice complex if there is a suitable trasformation that maps the point configurations of the two Wyckoff positions onto each other and if their space groups belong to the same <ins class="diffchange diffchange-inline">[[</ins>crystal family<ins class="diffchange diffchange-inline">]]</ins>. The 72 (in E<sup>2</sup>) or 1731 (in E<sup>3</sup>) Wyckoff positions are classified in 51 (E<sup>2</sup>) or 1128 (E<sup>3</sup>) types of Wyckoff sets. They are assigned to 30 (E<sup>2</sup>) or 402 (E<sup>3</sup>) lattice complexes.</div></td></tr>
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MassimoNespolo