Table 9.8.3.4

Janssen, T.; Janner, A.; Looijenga-Vos, A.; Wolff, P. M. de

doi:10.1107/97809553602060000624

International
Tables for
Crystallography
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

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International Tables for Crystallography (2006). Vol. C. ch. 9.8, pp. 920-921

Table 9.8.3.4

T. Janssen,^a A. Janner,^a A. Looijenga-Vos^b and P. M. de Wolff^c ^‡

^a Institute for Theoretical Physics, University of Nijmegen, Toernooiveld, NL-6525 ED Nijmegen, The Netherlands,^bRoland Holstlaan 908, NL-2624 JK Delft, The Netherlands, and ^cMeermanstraat 126, 2614 AM, Delft, The Netherlands

Table 9.8.3.4 | top | pdf |
(2 + 1)- and (2 + 2)-Dimensional superspace groups

(a) (2 + 1)-Dimensional superspace groups. The number labelling the superspace group is denoted by n.m, where n is the number attached to the two-dimensional basic space group and m numbers the various superspace groups having the same basic space group. The symbol of the basic space group, the symbol for the three-dimensional point group, the number of the three-dimensional Bravais class to which the superspace group belongs (Table 9.8.3.1a) and the superspace-group symbol are also given.

No.	Basic space group	Point group K_s	Bravais class No.	Group symbol
Oblique
1.1	p1	(1, 1)	1	p1(αβ)
2.1	p2	(2, $[{\bar 1}]$ )	1	p2(αβ)
Rectangular
3.1	pm	(m, 1)	2	pm1(0β)
3.2			2	pm1(0β)s0
3.3			3	pm1( $[{{1}\over{2}}]$ β)
3.4		(m, $[{\bar 1}]$ )	2	p1m(0β)
3.5			3	p1m( $[{{1}\over{2}}]$ β)
4.1	pg	(m, 1)	2	pg1(0β)
4.2			3	pg1( $[{{1}\over{2}}]$ β)
4.3		(m, $[{\bar 1}]$ )	2	p1g(0β)
5.1	cm	(m, 1)	4	cm1(0β)
5.2			4	cm1(0β)s0
5.3		(m, $[{\bar 1}]$ )	4	c1m(0β)
6.1	pmm	(mm, $[1{\bar 1}]$ )	2	pmm(0β)
6.2			2	pmm(0β)s0
6.3			3	pmm( $[{{1}\over{2}}]$ β)
7.1	pmg	(mm, $[1{\bar 1}]$ )	2	pmg(0β)
7.2			2	pgm(0β)
7.3			3	pgm( $[{{1}\over{2}}]$ β)
8.1	pgg	(mm, $[1{\bar 1}]$ )	2	pgg(0β)
9.1	cmm	(mm, $[1{\bar 1}]$ )	4	cmm(0β)
9.2			4	cmm(0β)s0

(b) (2 + 2)-Dimensional superspace groups. The number labelling the superspace group is denoted by n.m, where n is the number attached to the two-dimensional basic space group and m numbers the various superspace groups having the same basic space group. The symbol of the basic space group, the symbol for the four-dimensional point group, the number of the four-dimensional Bravais class to which the superspace group belongs (Table 9.8.3.1b) and the superspace-group symbol are also given.

No.	Basic space group	Point group K_s	Bravais class No.	Group symbol
Oblique
1.1	p1	(1, 1)	1	p1(αβ, λμ)
2.1	p2	(2, 2)	1	p2(αβ, λμ)
Rectangular
3.1	pm	(m, 1)	2	pm1(0β, 0μ)
3.2			2	pm1(0β, 0μ)s0, 0
3.3			3	pm1( $[{{1}\over{2}}]$ β, 0μ)
3.4			3	pm1( $[{{1}\over{2}}]$ β, 0μ)s0, 0
3.5		(m, 2)	2	p1m(0β, 0μ)
3.6			3	p1m( $[{{1}\over{2}}]$ β, 0μ)
3.7		(m, m)	4	pm1(α0, 0μ)
3.8			4	pm1(α0, 0μ)0s, 0
3.9			5	pm1(α $[{{1}\over{2}}]$ , 0μ)
3.10			5	pm1(α $[{{1}\over{2}}]$ , 0μ)0s, 0
3.11			5	p1m(α $[{{1}\over{2}}]$ , 0μ)
3.12			5	p1m(α $[{{1}\over{2}}]$ , 0μ)0, s0
3.13			6	pm1(α $[{{1}\over{2}}]$ , $[{{1}\over{2}}]$ μ)
3.14			7	pm1(αβ)
4.1	pg	(m, 1)	2	pg1(0β, 0μ)
4.2			3	pg1( $[{{1}\over{2}}]$ β, 0μ)
4.3		(m, 2)	2	p1g(0β, 0μ)
4.4		(m, m)	4	pg1(α0, 0μ)
4.5			7	pg1(α $[{{1}\over{2}}]$ , $[{{1}\over{2}}]$ μ)
5.1	cm	(m, 1)	8	cm1(0β, 0μ)
5.2			8	cm1(0β, 0μ)s0, 0
5.3		(m, 2)	8	c1m(0β, 0μ)
5.4		(m, m)	9	cm1(α0, 0μ)
5.5			9	cm1(α0, 0μ)0s, 0
5.6			10	cm(αβ)
6.1	pmm	(mm, 12)	2	pmm(0β, 0μ)
6.2			2	pmm(0β, 0μ)s0, 0
6.3			3	pmm( $[{{1}\over{2}}]$ β, 0μ)
6.4			3	pmm( $[{{1}\over{2}}]$ β, 0μ)s0, 0
6.5		(mm, mm)	4	pmm(α0, 0μ)
6.6			4	pmm(α0, 0μ)0s, 0
6.7			4	pmm(α0, 0μ)0s, s0
6.8			5	pmm(α $[{{1}\over{2}}]$ , 0μ)
6.9			5	pmm(α $[{{1}\over{2}}]$ , 0μ)0s, 0
6.10			6	pmm(α $[{{1}\over{2}}]$ , $[{{1}\over{2}}]$ μ)
6.11			7	pmm(αβ)
7.1	pmg	(mm, 12)	2	pmg(0β, 0μ)
7.2			2	pmg(0β, 0μ)0s, 0
7.3			2	pgm(0β, 0μ)
7.4			3	pgm( $[{{1}\over{2}}]$ β, 0μ)
7.5		(mm, mm)	4	pgm(α0, 0μ)
7.6			4	pgm(α0, 0μ)0, s0
7.7			5	pmg(α $[{{1}\over{2}}]$ , 0μ)
7.8			5	pmg(α $[{{1}\over{2}}]$ , 0μ)0s, 0
7.9			7	pgm(αβ)
8.1	pgg	(mm, 12)	2	pgg(0β, 0μ)
8.2		(mm, mm)	4	pgg(α0, 0μ)
8.3			7	pgg(αβ)
9.1	cmm	(mm, 12)	8	cmm(0β, 0μ)
9.2			8	cmm(0β, 0μ)0s, 0
9.3		(mm, mm)	9	cmm(α0, 0μ)
9.4			9	cmm(α0, 0μ)0s, 0
9.5			9	cmm(α0, 0μ)0s, s0
9.6			10	cmm(αβ)
Tetragonal
10.1	p4	(4, 4)	11	p4(αβ)
11.1	p4m	(4m, 4m)	12	p4m(α0)
11.2			12	p4m(α0)0, 0s
11.3			13	p4m(α $[{{1}\over{2}}]$ )
11.4		( $[4\dot m]$ , $[4\ddot m]$ )	14	p4m(αα)
11.5			14	p4m(αα)0, 0s
12.1	p4g	(4m, 4m)	12	p4g(α0)
12.2			12	p4g(α0), 0s
12.3		( $[4\dot m]$ , $[4\ddot m]$ )	14	p4g(αα)
12.4			14	p4g(αα)0, 0s
Hexagonal
13.1	p3	(3, 3)	15	p3(αβ)
14.1	p3m1	(3m, 3m)	16	p3m1(α0)
14.2		( $[3\dot m]$ , $[3\ddot m]$ )	17	p3m1(αα)
15.1	p31m	(3m, 3m)	16	p31m(α0)
16.1	p6	(6, 6)	15	p6(αβ)
17.1	p6m	(6m, 6m)	16	p6m(α0)
17.2		( $[6\dot m]$ , $[6\ddot m]$ )	17	p6m(αα)