Table 1.3.3.1

Souvignier, B.

doi:10.1107/97809553602060000921

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

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International Tables for Crystallography (2016). Vol. A. ch. 1.3, p. 29

Table 1.3.3.1

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: souvi@math.ru.nl

Table 1.3.3.1 | top | pdf |
Automorphism groups of two-dimensional primitive lattices

Lattice	Metric tensor	Bravais group
Lattice	Metric tensor	Hermann–Mauguin symbol	Generators
Oblique	$[\pmatrix{g_{11} & g_{12}\cr & g_{22}} ]$	2	2: $[\bar x, \bar y]$
Rectangular	$[\pmatrix{g_{11} & 0 \cr & g_{22} } ]$	2mm	2: $[\bar x, \bar y]$
	$[\pmatrix{g_{11} & 0 \cr & g_{22} } ]$		m₁₀: $[\bar x, y]$
Square	$[\pmatrix{g_{11} & 0 \cr & g_{11} } ]$	4mm	4⁺: $[\bar y, x]$
	$[\pmatrix{g_{11} & 0 \cr & g_{11} } ]$		m₁₀: $[\bar x, y]$
Hexagonal	$[\pmatrix{g_{11} & -{{1}\over{2}} g_{11} \cr & g_{11} } ]$	6mm	6⁺:
	$[\pmatrix{g_{11} & -{{1}\over{2}} g_{11} \cr & g_{11} } ]$		m₂₁: $[\bar x, \bar x + y]$