Table 1.3.3.2

Souvignier, B.

doi:10.1107/97809553602060000921

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

International Tables for Crystallography (2016). Vol. A. ch. 1.3, p. 30

Table 1.3.3.2

B. Souvignier^a ^*

^a Radboud University Nijmegen, Faculty of Science, Mathematics and Computing Science, Institute for Mathematics, Astrophysics and Particle Physics, Postbus 9010, 6500 GL Nijmegen, The Netherlands
Correspondence e-mail: [email protected]

Table 1.3.3.2 | top | pdf |
Automorphism groups of three-dimensional primitive lattices

Lattice	Metric tensor	Bravais group
Lattice	Metric tensor	Hermann–Mauguin symbol	Generators
Triclinic	$[\pmatrix{ g_{11} & g_{12} & g_{13} \cr & g_{22} & g_{23} \cr & & g_{33} } ]$	$[\bar{1}]$	$[\bar{1}{:}\ \bar x,\bar y,\bar z]$
Monoclinic	$[\pmatrix{ g_{11} & 0 & g_{13} \cr & g_{22} & 0 \cr & & g_{33} } ]$	2/m	$[2_{010}{:}\ \bar x,y,\bar z]$
			$[m_{010}{:}\ x,\bar y,z]$
Orthorhombic	$[\pmatrix{ g_{11} & 0 & 0 \cr & g_{22} & 0 \cr & & g_{33} } ]$	mmm	$[m_{100}{:} \ \bar x,y,z ]$
			$[m_{010}{:}\ x,\bar y,z]$
			$[m_{001}{:} \ x,y,\bar z]$
Tetragonal	$[\pmatrix{ g_{11} & 0 & 0 \cr & g_{11} & 0 \cr & & g_{33} } ]$	4/mmm	$[4_{001}{:}\ \bar y,x,z]$
			$[m_{001}{:} \ x,y,\bar z]$
			$[m_{100}{:} \ \bar x,y,z]$
Hexagonal	$[\pmatrix{ g_{11} & -{{1}\over{2}} g_{11} & 0 \cr & g_{11} & 0 \cr & & g_{33} } ]$	6/mmm	$[6_{001}{:}\ x-y,x,z]$
			$[m_{001}{:}\ x,y,\bar z]$
			$[m_{100}{:}\ \bar x+y,y,z]$
Rhombohedral	$[\pmatrix{ g_{11} & g_{12} & g_{12} \cr & g_{11} & g_{12} \cr & & g_{11} } ]$	$[\bar{3}m]$	$[\bar{3}_{111}{:}\ \bar z,\bar x,\bar y]$
			$[m_{1\bar{1}0}{:}\ y,x,z ]$
Cubic	$[\pmatrix{ g_{11} & 0 & 0 \cr & g_{11} & 0 \cr & & g_{11} } ]$	$[m\bar{3}m]$	$[m_{001}{:} \ x,y,\bar z]$
			$[\bar{3}_{111}{:}\ \bar z,\bar x,\bar y]$
			$[m_{110}{:} \ \bar y,\bar x,z]$