Table 10.1.4.1

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. 798

Table 10.1.4.1

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 10.1.4.1 | top | pdf |
Classes of general point groups in two dimensions (N = integer $[\geq]$ 0)

General Hermann–Mauguin symbol	Order of group	General edge form	General point form	Crystallographic groups
4N-gonal system (n-fold rotation point with )
n	n	Regular n-gon	Regular n-gon	4
nmm	2n	Semiregular di-n-gon	Truncated n-gon	4mm
-gonal system (n-fold or $[{1 \over 2}n]$ -fold rotation point with )
$[{1 \over 2}n]$	$[{1 \over 2}n]$	Regular $[{1 \over 2}n]$ -gon	Regular $[{1 \over 2}n]$ -gon	1, 3
$[{1 \over 2}nm]$	n	Semiregular di- $[{1 \over 2}n]$ -gon	Truncated $[{1 \over 2}n]$ -gon	m, 3m
n	n	Regular n-gon	Regular n-gon	2, 6
nmm	2n	Semiregular di-n-gon	Truncated n-gon	2mm, 6mm
Circular system ^†
∞	∞	Rotating circle	Rotating circle	–
∞m	∞	Stationary circle	Stationary circle	–

^†A rotating circle has no mirror lines; there exist two enantiomorphic circles with opposite senses of rotation. A stationary circle has infinitely many mirror lines through its centre.