Hahn Th. (ed.) International tables for crystallography. Vol. A. Space-group symmetry
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Pcc2 C
3
2v
mm2 Orthorhombic
No. 27 Pcc2
Patterson symmetry Pmmm
Origin on cc2
Asymmetric unit 0 ≤ x ≤
1
2
;0≤ y ≤
1
2
;0≤ z ≤ 1
Symmetry operations
(1) 1 (2) 2 0,0,z (3) cx,0, z (4) c 0, y,z
222
International Tables for Crystallography (2006). Vol. A, Space group 27, pp. 222–223.
Copyright © 2006 International Union of Crystallography
CONTINUED No. 27 Pcc2
Generators selected (1); t(1, 0,0); t(0,1,0); t(0,0,1); (2); (3)
Positions
Multiplicity,
Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
General:
4 e 1(1)x,y,z (2) ¯x, ¯y,z (3) x, ¯y, z +
1
2
(4) ¯x,y, z +
1
2
0kl : l = 2n
h0l : l = 2n
00l : l = 2n
Special: as above, plus
2 d ..2
1
2
,
1
2
,z
1
2
,
1
2
,z +
1
2
hkl : l = 2n
2 c ..2
1
2
,0, z
1
2
,0, z +
1
2
hkl : l = 2n
2 b ..20,
1
2
,z 0,
1
2
,z +
1
2
hkl : l = 2n
2 a ..20,0,z 0,0,z +
1
2
hkl : l = 2n
Symmetry of special projections
Along [001] p2mm
a
= ab
= b
Origin at 0,0,z
Along [100] p1m1
a
= bb
=
1
2
c
Origin at x,0,0
Along [010] p11m
a
=
1
2
cb
= a
Origin at 0,y, 0
Maximal non-isomorphic subgroups
I
[2] P1c1(Pc,7) 1; 3
[2] Pc11(Pc,7) 1; 4
[2] P112 (P2, 3) 1; 2
IIa none
IIb [2] Pcn2(a
= 2a)(Pnc2, 30); [2] Pnc2(b
= 2b) (30); [2] Ccc2(a
= 2a,b
= 2b) (37)
Maximal isomorphic subgroups of lowest index
IIc
[2] Pcc2(a
= 2a or b
= 2b) (27); [3] Pcc2(c
= 3c) (27)
Minimal non-isomorphic supergroups
I
[2] Pccm (49); [2] Pcca (54); [2] Pccn(56); [2] P4
2
cm (101); [2] P4cc (103); [2] P
¯
4c2 (116)
II [2] Ccc2 (37); [2] Aem2 (39); [2] Bme2(Aem2, 39); [2] Iba2 (45); [2] Pmm2(c
=
1
2
c) (25)
223
Pma2 C
4
2v
mm2 Orthorhombic
No. 28 Pma2
Patterson symmetry Pmmm
Origin on 1a2
Asymmetric unit 0 ≤ x ≤
1
4
;0≤ y ≤ 1; 0 ≤ z ≤ 1
Symmetry operations
(1) 1 (2) 2 0,0,z (3) ax,0,z (4) m
1
4
,y,z
224
International Tables for Crystallography (2006). Vol. A, Space group 28, pp. 224–225.
Copyright © 2006 International Union of Crystallography
CONTINUED No. 28 Pma2
Generators selected (1); t(1, 0,0); t(0,1,0); t(0,0,1); (2); (3)
Positions
Multiplicity,
Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
General:
4 d 1(1)x,y,z (2) ¯x, ¯y,z (3) x +
1
2
, ¯y, z (4) ¯x +
1
2
,y,zh0l : h = 2n
h00 : h = 2n
Special: as above, plus
2 cm..
1
4
,y,z
3
4
, ¯y, z no extra conditions
2 b ..20,
1
2
,z
1
2
,
1
2
,zhkl: h = 2n
2 a ..20,0, z
1
2
,0, zhkl: h = 2n
Symmetry of special projections
Along [001] p2mg
a
= ab
= b
Origin at 0,0,z
Along [100] p1m1
a
= bb
= c
Origin at x, 0,0
Along [010] p11m
a
= cb
=
1
2
a
Origin at 0,y, 0
Maximal non-isomorphic subgroups
I
[2] P1a1(Pc,7) 1; 3
[2] Pm11(Pm,6) 1; 4
[2] P112 (P2, 3) 1; 2
IIa none
IIb [2] Pba2(b
= 2b) (32); [2] Pmn2
1
(c
= 2c) (31); [2] Pcn2(c
= 2c)(Pnc2, 30); [2] Pca2
1
(c
= 2c) (29);
[2] Aea2(b
= 2b,c
= 2c) (41); [2] Ama2(b
= 2b,c
= 2c) (40)
Maximal isomorphic subgroups of lowest index
IIc
[2] Pma2(b
= 2b) (28); [2] Pma2(c
= 2c) (28); [3] Pma2(a
= 3a) (28)
Minimal non-isomorphic supergroups
I
[2] Pccm (49); [2] Pmma (51); [2] Pmna(53); [2] Pbcm (57)
II [2] Cmm2 (35); [2] Bme2(Aem2, 39); [2] Ama2 (40); [2] Ima2 (46); [2] Pmm2(a
=
1
2
a) (25)
225
Pca2
1
C
5
2v
mm2 Orthorhombic
No. 29 Pca2
1
Patterson symmetry Pmmm
Origin on 1a2
1
Asymmetric unit 0 ≤ x ≤
1
4
;0≤ y ≤ 1; 0 ≤ z ≤ 1
Symmetry operations
(1) 1 (2) 2(0, 0,
1
2
) 0,0,z (3) ax,0,z (4) c
1
4
,y,z
226
International Tables for Crystallography (2006). Vol. A, Space group 29, pp. 226–227.
Copyright © 2006 International Union of Crystallography
CONTINUED No. 29 Pca2
1
Generators selected (1); t(1, 0,0); t(0,1,0); t(0,0,1); (2); (3)
Positions
Multiplicity,
Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
General:
4 a 1(1)x, y,z (2) ¯x, ¯y,z +
1
2
(3) x +
1
2
, ¯y, z (4) ¯x+
1
2
,y,z +
1
2
0kl : l = 2n
h0l : h = 2n
h00 : h = 2n
00l : l = 2n
Symmetry of special projections
Along [001] p2mg
a
= ab
= b
Origin at 0,0,z
Along [100] p1m1
a
= bb
=
1
2
c
Origin at x,0,0
Along [010] p11g
a
= cb
=
1
2
a
Origin at 0,y, 0
Maximal non-isomorphic subgroups
I
[2] P1a1(Pc,7) 1; 3
[2] Pc11(Pc,7) 1; 4
[2] P112
1
(P2
1
,4) 1; 2
IIa none
IIb [2] Pna2
1
(b
= 2b) (33)
Maximal isomorphic subgroups of lowest index
IIc
[2] Pca2
1
(b
= 2b) (29); [3] Pca2
1
(a
= 3a) (29); [3] Pca2
1
(c
= 3c) (29)
Minimal non-isomorphic supergroups
I
[2] Pcca (54); [2] Pbcm (57); [2] Pbcn (60); [2] Pbca (61)
II [2] Ccm2
1
(Cmc2
1
, 36); [2] Bme2(Aem2, 39); [2] Aea2 (41); [2] Iba2 (45); [2] Pcm2
1
(a
=
1
2
a)(Pmc2
1
, 26);
[2] Pma2(c
=
1
2
c) (28)
227
Pnc2 C
6
2v
mm2 Orthorhombic
No. 30 Pnc2
Patterson symmetry Pmmm
Origin on n12
Asymmetric unit 0 ≤ x ≤
1
2
;0≤ y ≤ 1; 0 ≤ z ≤
1
2
Symmetry operations
(1) 1 (2) 2 0,0,z (3) cx,
1
4
,z (4) n(0,
1
2
,
1
2
) 0,y,z
228
International Tables for Crystallography (2006). Vol. A, Space group 30, pp. 228–229.
Copyright © 2006 International Union of Crystallography
CONTINUED No. 30 Pnc2
Generators selected (1); t(1, 0,0); t(0,1,0); t(0,0,1); (2); (3)
Positions
Multiplicity,
Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
General:
4 c 1(1)x,y,z (2) ¯x, ¯y,z (3) x, ¯y +
1
2
,z +
1
2
(4) ¯x,y +
1
2
,z +
1
2
0kl : k + l = 2 n
h0l : l = 2n
0k0: k = 2n
00l : l = 2n
Special: as above, plus
2 b ..2
1
2
,0, z
1
2
,
1
2
,z +
1
2
hkl : k + l = 2n
2 a ..20,0,z 0,
1
2
,z +
1
2
hkl : k + l = 2n
Symmetry of special projections
Along [001] p2gm
a
= ab
= b
Origin at 0,0,z
Along [100] c1m1
a
= bb
= c
Origin at x,0,0
Along [010] p11m
a
=
1
2
cb
= a
Origin at 0,y, 0
Maximal non-isomorphic subgroups
I
[2] P1c1(Pc,7) 1; 3
[2] Pn11(Pc,7) 1; 4
[2] P112 (P2, 3) 1; 2
IIa none
IIb [2] Pnn2(a
= 2a) (34)
Maximal isomorphic subgroups of lowest index
IIc
[2] Pnc2(a
= 2a) (30); [3] Pnc2(b
= 3b) (30); [3] Pnc2(c
= 3c) (30)
Minimal non-isomorphic supergroups
I
[2] Pban(50); [2] Pnna (52); [2] Pmna (53); [2] Pbcn (60)
II [2] Ccc2 (37); [2] Amm2 (38); [2] Bbe2(Aea2, 41); [2] Ima2 (46); [2] Pcc2(b
=
1
2
b) (27); [2] Pbm2(c
=
1
2
c)(Pma2, 28)
229
Pmn2
1
C
7
2v
mm2 Orthorhombic
No. 31 Pmn2
1
Patterson symmetry Pmmm
Origin on mn1
Asymmetric unit 0 ≤ x ≤
1
2
;0≤ y ≤
1
2
;0≤ z ≤ 1
Symmetry operations
(1) 1 (2) 2(0, 0,
1
2
)
1
4
,0, z (3) n(
1
2
,0,
1
2
) x,0,z (4) m 0,y,z
230
International Tables for Crystallography (2006). Vol. A, Space group 31, pp. 230–231.
Copyright © 2006 International Union of Crystallography
CONTINUED No. 31 Pmn2
1
Generators selected (1); t(1, 0,0); t(0,1,0); t(0,0,1); (2); (3)
Positions
Multiplicity,
Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
General:
4 b 1(1)x, y,z (2) ¯x +
1
2
, ¯y, z +
1
2
(3) x +
1
2
, ¯y, z +
1
2
(4) ¯x,y, zh0l : h + l = 2n
h00 : h = 2n
00l : l = 2n
Special: no extra conditions
2 am.. 0, y,z
1
2
, ¯y, z +
1
2
Symmetry of special projections
Along [001] p2mg
a
= ab
= b
Origin at
1
4
,0, z
Along [100] p1g1
a
= bb
= c
Origin at x,0,0
Along [010] c11m
a
= cb
= a
Origin at 0,y, 0
Maximal non-isomorphic subgroups
I
[2] P1n1(Pc,7) 1; 3
[2] Pm11(Pm,6) 1; 4
[2] P112
1
(P2
1
,4) 1; 2
IIa none
IIb [2] Pbn2
1
(b
= 2b)(Pna2
1
, 33)
Maximal isomorphic subgroups of lowest index
IIc
[2] Pmn2
1
(b
= 2b) (31); [3] Pmn2
1
(a
= 3a) (31); [3] Pmn2
1
(c
= 3c) (31)
Minimal non-isomorphic supergroups
I
[2] Pmna (53); [2] Pnnm(58); [2] Pmmn (59); [2] Pnma (62)
II [2] Cmc2
1
(36); [2] Bmm2(Amm2, 38); [2] Ama2 (40); [2] Imm2 (44); [2] Pmc2
1
(a
=
1
2
a) (26); [2] Pma2(c
=
1
2
c) (28)
231