View source for Arithmetic crystal class

= Arithmetic crystal classes =


=== Other languages ===

Classes arithmétiques (''Fr'').


== Definition ==

<table border cellspacing=0 cellpadding=5 align=center>
 <caption align=top> '''Three-dimensional arithmetic crystal classes.''' </caption>
 <tr align=center>
    <th rowspan=3> Crystal systems</th>
    <th colspan=3> Crystal class</th>
 </tr>
 <tr align=center>
    <th rowspan=1 > Geometric</th>
    <th colspan=2> Arithmetic</th>
 </tr>
 <tr align=center>
    <th> </th>
    <th> Number </th>
    <th> Symbol </th>
  </tr>
 <tr align=center>
   <td rowspan=2>Triclinic</td>
   <td><math> 1 </math></td>
   <td> 1 </td>
   <td><math> 1P </math></td>
   </tr>
 <tr align=center>
    <td><math> {\bar 1} </math></td>
   <td> 2 </td>
   <td><math> {\bar 1}P </math></td>
 </tr>
 <tr align=center>
   <td rowspan=6>Monoclinic</td>
   <td><math> 2 </math></td>
   <td> 3 </td>
   <td><math> 2P </math></td>
   </tr>
 <tr align=center>
    <td rowspan=2><math> m </math></td>
   <td> 4 </td>
   <td><math> 2C </math></td>
 </tr>
<tr align=center>
   <td> 5 </td>
   <td><math> mP </math></td>
</tr>
<tr align=center>
    <td rowspan=3><math> 2/m </math></td>
   <td> 6 </td>
   <td><math> mC </math></td>
</tr>
<tr align=center>
   <td> 7 </td>
   <td><math> 2/m P </math></td>
 </tr>
<tr align=center>
   <td> 8 </td>
   <td><math> 2/m C </math></td>
</tr>
<tr align=center>
   <td rowspan=14>Orthorhombic</td>
   <td rowspan=4><math> 222 </math></td>
   <td> 9 </td>
   <td><math> 222 P </math></td>
   </tr>
 <tr align=center>
   <td> 10 </td>
   <td><math> 222 C </math></td>
 </tr>
<tr align=center>
   <td> 11 </td>
   <td><math> 222 F </math></td>
</tr>
<tr align=center>
   <td> 12 </td>
   <td><math> 222 I </math></td>
</tr>
<tr align=center>
    <td rowspan=6><math> mm </math></td>
   <td> 13 </td>
   <td><math> mm2 P </math></td>
 </tr>
<tr align=center>
   <td> 14 </td>
   <td><math> mm2 C </math></td>
</tr>
<tr align=center>
   <td rowspan=2> 15 </td>
   <td><math> 2mmC </math></td>
</tr>
<tr align=center>
   <td><math> (Amm2)  </math></td>
</tr>
<tr align=center>
   <td> 16 </td>
   <td><math> mm2F </math></td>
</tr>
<tr align=center>
   <td> 17 </td>
   <td><math> mm2I </math></td>
</tr>
<tr align=center>
  <td rowspan=4><math> mmm </math></td>
   <td> 18 </td>
   <td><math> mmmP </math></td>
   </tr>
<tr align=center>
   <td> 19 </td>
   <td><math> mmmC </math></td>
   </tr>
<tr align=center>
   <td> 20 </td>
   <td><math> mmmF </math></td>
   </tr>
<tr align=center>
   <td> 21 </td>
   <td><math> mmmI </math></td>
   </tr>
<tr align=center>
   <td rowspan=16>Tetragonal</td>
   <td rowspan=2><math> 4 </math></td>
   <td> 22 </td>
   <td><math> 4P </math></td>
   </tr>
<tr align=center>
   <td> 23 </td>
   <td><math> 4I </math></td>
   </tr>
<tr align=center>
   <td rowspan=2><math> {\bar 4} </math></td>
   <td> 24 </td>
   <td><math> {\bar 4}P </math></td>
   </tr>
<tr align=center>
   <td> 25 </td>
   <td><math> {\bar 4}I </math></td>
   </tr>
<tr align=center>
   <td rowspan=2><math> 4/m </math></td>
   <td> 26 </td>
   <td><math> 4/mP </math></td>
   </tr>
<tr align=center>
   <td> 27 </td>
   <td><math> 4/mI </math></td>
   </tr>
<tr align=center>
   <td rowspan=2><math> 422 </math></td>
   <td> 28 </td>
   <td><math> 422P </math></td>
   </tr>
<tr align=center>
   <td> 29 </td>
   <td><math> 422I </math></td>
   </tr>
<tr align=center>
   <td rowspan=2><math> 4mm </math></td>
   <td> 30 </td>
   <td><math> 4mmP </math></td>
   </tr>
<tr align=center>
   <td> 31 </td>
   <td><math> 4mmI </math></td>
   </tr>
<tr align=center>
   <td rowspan=4><math> {\bar 4}m </math></td>
   <td> 32 </td>
   <td><math> {\bar 4}2mP </math></td>
   </tr>
<tr align=center>
   <td> 33 </td>
   <td><math> {\bar 4}m2P </math></td>
   </tr>
<tr align=center>
   <td> 34 </td>
   <td><math> {\bar 4}m2I </math></td>
   </tr>
<tr align=center>
   <td> 35 </td>
   <td><math> {\bar 4}2mI </math></td>
   </tr>
<tr align=center>
   <td rowspan=2><math> 4/mmm </math></td>
   <td> 36 </td>
   <td><math> 4/mmmP </math></td>
   </tr>
<tr align=center>
   <td> 37 </td>
   <td><math> 4/mmmI </math></td>
   </tr>
<tr align=center>
   <td rowspan=13>Trigonal</td>
   <td rowspan=2><math> 3 </math></td>
   <td> 38 </td>
   <td><math> 3P </math></td>
   </tr>
<tr align=center>
   <td> 39 </td>
   <td><math> 3R </math></td>
   </tr>
<tr align=center>
   <td rowspan=2><math> {\bar 3} </math></td>
   <td> 40 </td>
   <td><math> {\bar 3}P </math></td>
   </tr>
<tr align=center>
   <td> 41 </td>
   <td><math> {\bar 3}R </math></td>
   </tr>
<tr align=center>
   <td rowspan=3><math> 32 </math></td>
   <td> 42 </td>
   <td><math> 312P </math></td>
   </tr>
<tr align=center>
   <td> 43 </td>
   <td><math> 321P </math></td>
   </tr>
<tr align=center>
   <td> 44 </td>
   <td><math> 32R </math></td>
   </tr>
<tr align=center>
   <td rowspan=3><math> 3m </math></td>
   <td> 45 </td>
   <td><math> 3m1P </math></td>
   </tr>
<tr align=center>
   <td> 46 </td>
   <td><math> 31mP </math></td>
   </tr>
<tr align=center>
   <td> 47 </td>
   <td><math> 3mR </math></td>
   </tr>
<tr align=center>
   <td rowspan=3><math> {\bar 3}m </math></td>
   <td> 48 </td>
   <td><math> {\bar 3}1mP </math></td>
   </tr>
<tr align=center>
   <td> 49 </td>
   <td><math> {\bar 3}m1P </math></td>
   </tr>
<tr align=center>
   <td> 50 </td>
   <td><math> {\bar 3}mR </math></td>
   </tr>

</table> 

=== See also ===

Section 8.2.3 of ''International Tables of Crystallography, Volume A''<br>
Sections 1.3.4 and 1.5.3 of ''International Tables of Crystallography, Volume B''<br>
Section 1.4 of ''International Tables of Crystallography, Volume C''<br>


[[Category:Fundamental crystallography]]