Table 10.1.2.4

Hahn, Th.; Klapper, H.

doi:10.1107/97809553602060000520

International
Tables for
Crystallography
Volume A
Space-group symmetry
Edited by Th. Hahn

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International Tables for Crystallography (2006). Vol. A. ch. 10.1, p. 794

Table 10.1.2.4

Th. Hahn^a ^* and H. Klapper^a ^‡

^a Institut für Kristallographie, Rheinisch-Westfälische Technische Hochschule, Aachen, Germany
Correspondence e-mail: hahn@xtl.rwth-aachen.de

Table 10.1.2.4 | top | pdf |
Names and symbols of the 32 crystal classes

System used in this volume	Point group		Schoenflies symbol	Class names
	International symbol			Class names
	Short	Full		Groth (1921)	Friedel (1926)
Triclinic	1	1	$[C_{1}]$	Pedial (asymmetric)	Hemihedry
Triclinic	$[\overline{1}]$	$[\overline{1}]$	$[C_{i}(S_{2})]$	Pinacoidal	Holohedry
Monoclinic	2	2	$[C_{2}]$	Sphenoidal	Holoaxial hemihedry
	m	m	$[C_{s}(C_{1h})]$	Domatic	Antihemihedry
		$[\displaystyle{2 \over m}]$	$[C_{2h}]$	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
		$[\displaystyle{4 \over m}]$	$[C_{4h}]$	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
		$[\displaystyle{6 \over m}]$	$[C_{6h}]$	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
		$[\displaystyle{6 \over m} {2 \over m} {2 \over m}]$	$[D_{6h}]$	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