Tables for
Volume A
Space-group symmetry
Edited by M. I. Aroyo

International Tables for Crystallography (2016). Vol. A, ch. 3.2, p. 728


Th. Hahna and H. Klappera

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Names and symbols of the 32 crystal classes

System used in this volumePoint groupSchoenflies symbolClass names
International symbol
ShortFullGroth (1921[link])Friedel (1926[link])
Triclinic 1 1 [C_{1}] Pedial (asymmetric) Hemihedry
[\overline{1}] [\overline{1}] [C_{i}(S_{2})] Pinacoidal Holohedry
Monoclinic 2 2 [C_{2}] Sphenoidal Holoaxial hemihedry
m m [C_{s}(C_{1h})] Domatic Antihemihedry
[2/m] [\displaystyle{2 \over m}] [C_{2h}] Prismatic Holohedry
Orthorhombic 222 222 [D_{2} (V)] Disphenoidal Holoaxial hemihedry
mm2 mm2 [C_{2v}] Pyramidal Antihemihedry
mmm [\displaystyle{2 \over m} {2 \over m} {2 \over m}] [D_{2h} (V_{h})] Dipyramidal Holohedry
Tetragonal 4 4 [C_{4}] Pyramidal Tetartohedry with 4-axis
[\overline{4}] [\overline{4}] [S_{4}] Disphenoidal Sphenohedral tetartohedry
[4/m] [\displaystyle{4 \over m}] [C_{4h}] Dipyramidal Parahemihedry
422 422 [D_{4}] Trapezohedral Holoaxial hemihedry
4mm 4mm [C_{4v}] Ditetragonal-pyramidal Antihemihedry with 4-axis
[\overline{4}2m] [\overline{4}2m] [D_{2d} (V_{d})] Scalenohedral Sphenohedral antihemihedry
4/mmm [\displaystyle{4 \over m} {2 \over m} {2 \over m}] [D_{4h}] Ditetragonal-dipyramidal Holohedry
          Hexagonal Rhombohedral
Trigonal 3 3 [C_{3}] Pyramidal Ogdohedry Tetartohedry
[\overline{3}] [\overline{3}] [C_{3i}(S_{6})] Rhombohedral Paratetartohedry Parahemihedry
32 32 [D_{3}] Trapezohedral Holoaxial tetartohedry with 3-axis Holoaxial hemihedry
3m 3m [C_{3v}] Ditrigonal-pyramidal Hemimorphic antitetartohedry Antihemihedry
[\overline{3}m] [\overline{3} \displaystyle{2 \over m}] [D_{3d}] Ditrigonal-scalenohedral Parahemihedry with 3-axis Holohedry
Hexagonal 6 6 [C_{6}] Pyramidal Tetartohedry with 6-axis
[\overline{6}] [\overline{6}] [C_{3h}] Trigonal-dipyramidal Trigonohedral antitetartohedry
[6/m] [\displaystyle{6 \over m}] [C_{6h}] Dipyramidal Parahemihedry with 6-axis
622 622 [D_{6}] Trapezohedral Holoaxial hemihedry
6mm 6mm [C_{6v}] Dihexagonal-pyramidal Antihemihedry with 6-axis
[\overline{6}2m] [\overline{6}2m] [D_{3h}] Ditrigonal-dipyramidal Trigonohedral antihemihedry
[6/mmm] [\displaystyle{6 \over m} {2 \over m} {2 \over m}] [D_{6h}] Dihexagonal-dipyramidal Holohedry
Cubic 23 23 T [\!\matrix{\hbox{Tetrahedral-pentagondodecahedral}\hfill\cr\quad (=\hbox{tetartoidal})\hfill\cr}] Tetartohedry
[m\overline{3}] [\displaystyle{2 \over m} \overline{3}] [T_{h}] [\!\matrix{\hbox{Disdodecahedral}\hfill\cr\quad(=\hbox{diploidal})\hfill\cr}] Parahemihedry
432 432 O [\!\matrix{\hbox{Pentagon-icositetrahedral}\hfill\cr\quad(=\hbox{gyroidal})\hfill\cr}] Holoaxial hemihedry
[\overline{4}3m] [\overline{4}3m] [T_{d}] [\!\matrix{\hbox{Hexakistetrahedral}\hfill\cr \quad(=\hbox{hextetrahedral})\hfill\cr}] Antihemihedry
[m\overline{3}m] [\displaystyle{4 \over m} \overline{3} {2 \over m}] [O_{h}] [\!\matrix{\hbox{Hexakisoctahedral}\hfill\cr\quad(=\hbox{hexoctahedral})\hfill\cr}] Holohedry