# Arithmetic crystal classes

### Other languages

Classes arithmétiques (Fr).

## Definition

Three-dimensional arithmetic crystal classes.
Crystal systems Crystal class
Geometric Arithmetic
Number Symbol
Triclinic $1$ 1 $1P$
${\bar 1}$ 2 ${\bar 1}P$
Monoclinic $2$ 3 $2P$
$m$ 4 $2C$
5 $mP$
$2/m$ 6 $mC$
7 $2/m P$
8 $2/m C$
Orthorhombic $222$ 9 $222 P$
10 $222 C$
11 $222 F$
12 $222 I$
$mm$ 13 $mm2 P$
14 $mm2 C$
15 $2mmC$
$(Amm2)$
16 $mm2F$
17 $mm2I$
$mmm$ 18 $mmmP$
19 $mmmC$
20 $mmmF$
21 $mmmI$
Tetragonal $4$ 22 $4P$
23 $4I$
${\bar 4}$ 24 ${\bar 4}P$
25 ${\bar 4}I$
$4/m$ 26 $4/mP$
27 $4/mI$
$422$ 28 $422P$
29 $422I$
$4mm$ 30 $4mmP$
31 $4mmI$
${\bar 4}m$ 32 ${\bar 4}2mP$
33 ${\bar 4}m2P$
34 ${\bar 4}m2I$
35 ${\bar 4}2mI$
$4/mmm$ 36 $4/mmmP$
37 $4/mmmI$
Trigonal $3$ 38 $3P$
39 $3R$
${\bar 3}$ 40 ${\bar 3}P$
41 ${\bar 3}R$
$32$ 42 $312P$
43 $321P$
44 $32R$
$3m$ 45 $3m1P$
46 $31mP$
47 $3mR$
${\bar 3}m$ 48 ${\bar 3}1mP$
49 ${\bar 3}m1P$
50 ${\bar 3}mR$
Hexagonal $6$ 51 $6P$
${\bar 6}$ 52 ${\bar 6}P$
$6/m$ 53 $6/mP$
$622$ 54 $622P$
$6mm$ 55 $6mmP$
${\bar 6}m$ 56 ${\bar 6}2mP$
57 ${\bar 6}m2P$
$6/mmm$ 58 $6/mmm$
Cubic $23$ 59 $23P$
60 $23F$
61 $23I$
$m{\bar 3}$ 62 $m{\bar 3}P$
63 $m{\bar 3}F$
64 $m{\bar 3}I$
$432$ 65 $432P$
66 $432F$
67 $432I$
${\bar 4}3m$ 68 ${\bar 4}3m P$
69 ${\bar 4}3m F$
70 ${\bar 4}3m I$
$m{\bar 3}m$ 71 $m{\bar 3}mP$
72 $m{\bar 3}mF$
73 $m{\bar 3}mI$