C2 C23 2 Monoclinic No. 5 C121 Patterson symmetry C12/m1 UNIQUE AXIS b, CELL CHOICE 1

Origin on 2

 Asymmetric unit 0 ≤ x ≤ 1/2; 0 ≤ y ≤ 1/2; 0 ≤ z ≤ 1

Symmetry operations

For (0, 0, 0)+ set

 (1)  1 (2)  2   0, y, 0

For (1/21/2, 0)+ set

 (1)  t(1/2, 1/2, 0) (2)  2(0, 1/2, 0)   1/4, y, 0

Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); t(1/21/2, 0); (2)

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
(0, 0, 0)+  (1/21/2, 0)+  General:
 4 c 1
 (1) x, y, z (2) -x, y, -z
hkl : h + k = 2n
h0l : h = 2n
0kl : k = 2n
hk0 : h + k = 2n
0k0 : k = 2n
h00 : h = 2n
Special: as above, plus
 2 b 2
 0, y, 1/2
no extra conditions
 2 a 2
 0, y, 0
no extra conditions

Symmetry of special projections

 Along [001]   c1m1a' = ap   b' = b   Origin at 0, 0, z Along [100]   p11ma' = 1/2b   b' = cp   Origin at x, 0, 0 Along [010]   p2a' = c   b' = 1/2a   Origin at 0, y, 0

Maximal non-isomorphic subgroups

 I [2] C1 (P1, 1) 1+
 IIa [2] P1211 (P21, 4) 1; 2 + (1/2, 1/2, 0) [2] P121 (P2, 3) 1; 2
 IIb none

Maximal isomorphic subgroups of lowest index

 IIc [2] C121 (c' = 2c or a' = a + 2c, c' = 2c) (C2, 5); [3] C121 (b' = 3b) (C2, 5)

Minimal non-isomorphic supergroups

 I [2] C2/m (12); [2] C2/c (15); [2] C2221 (20); [2] C222 (21); [2] F222 (22); [2] I222 (23); [2] I212121 (24); [2] Amm2 (38); [2] Aem2 (39); [2] Ama2 (40); [2] Aea2 (41); [2] Fmm2 (42); [2] Fdd2 (43); [2] Imm2 (44); [2] Iba2 (45); [2] Ima2 (46); [2] I4 (79); [2] I41 (80); [2] I-4 (82); [3] P312 (149); [3] P321 (150); [3] P3112 (151); [3] P3121 (152); [3] P3212 (153); [3] P3221 (154); [3] R32 (155)
 II [2] P121 (a' = 1/2a, b' = 1/2b) (P2, 3)

UNIQUE AXIS b, DIFFERENT CELL CHOICES

C121

UNIQUE AXIS b, CELL CHOICE 1

Origin on 2

 Asymmetric unit 0 ≤ x ≤ 1/2; 0 ≤ y ≤ 1/2; 0 ≤ z ≤ 1

Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); t(1/21/2, 0); (2)

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
(0, 0, 0)+  (1/21/2, 0)+  General:
 4 c 1
 (1) x, y, z (2) -x, y, -z
hkl : h + k = 2n
h0l : h = 2n
0kl : k = 2n
hk0 : h + k = 2n
0k0 : k = 2n
h00 : h = 2n
Special: as above, plus
 2 b 2
 0, y, 1/2
no extra conditions
 2 a 2
 0, y, 0
no extra conditions

A121

UNIQUE AXIS b, CELL CHOICE 2

Origin on 2

 Asymmetric unit 0 ≤ x ≤ 1/2; 0 ≤ y ≤ 1/2; 0 ≤ z ≤ 1

Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); t(0, 1/21/2); (2)

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
(0, 0, 0)+  (0, 1/21/2)+  General:
 4 c 1
 (1) x, y, z (2) -x, y, -z
hkl : k + l = 2n
h0l : l = 2n
0kl : k + l = 2n
hk0 : k = 2n
0k0 : k = 2n
00l : l = 2n
Special: as above, plus
 2 b 2
 1/2, y, 1/2
no extra conditions
 2 a 2
 0, y, 0
no extra conditions

I121

UNIQUE AXIS b, CELL CHOICE 3

Origin on 2

 Asymmetric unit 0 ≤ x ≤ 1/2; 0 ≤ y ≤ 1/2; 0 ≤ z ≤ 1

Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); t(1/21/21/2); (2)

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
(0, 0, 0)+  (1/21/21/2)+  General:
 4 c 1
 (1) x, y, z (2) -x, y, -z
hkl : h + k + l = 2n
h0l : h + l = 2n
0kl : k + l = 2n
hk0 : h + k = 2n
0k0 : k = 2n
h00 : h = 2n
00l : l = 2n
Special: as above, plus
 2 b 2
 1/2, y, 0
no extra conditions
 2 a 2
 0, y, 0
no extra conditions

 C2 C23 2 Monoclinic No. 5 A112 Patterson symmetry A112/m UNIQUE AXIS c, CELL CHOICE 1

Origin on 2

 Asymmetric unit 0 ≤ x ≤ 1; 0 ≤ y ≤ 1/2; 0 ≤ z ≤ 1/2

Symmetry operations

For (0, 0, 0)+ set

 (1)  1 (2)  2   0, 0, z

For (0, 1/21/2)+ set

 (1)  t(0, 1/2, 1/2) (2)  2(0, 0, 1/2)   0, 1/4, z

Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); t(0, 1/21/2); (2)

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
(0, 0, 0)+  (0, 1/21/2)+  General:
 4 c 1
 (1) x, y, z (2) -x, -y, z
hkl : k + l = 2n
hk0 : k = 2n
0kl : k + l = 2n
h0l : l = 2n
00l : l = 2n
0k0 : k = 2n
Special: as above, plus
 2 b 2
 1/2, 0, z
no extra conditions
 2 a 2
 0, 0, z
no extra conditions

Symmetry of special projections

 Along [001]   p2a' = a   b' = 1/2b   Origin at 0, 0, z Along [100]   c1m1a' = bp   b' = c   Origin at x, 0, 0 Along [010]   p11ma' = 1/2c   b' = ap   Origin at 0, y, 0

Maximal non-isomorphic subgroups

 I [2] A1 (P1, 1) 1+
 IIa [2] P1121 (P21, 4) 1; 2 + (0, 1/2, 1/2) [2] P112 (P2, 3) 1; 2
 IIb none

Maximal isomorphic subgroups of lowest index

 IIc [2] A112 (a' = 2a or a' = 2a, b' = 2a + b) (C2, 5); [3] A112 (c' = 3c) (C2, 5)

Minimal non-isomorphic supergroups

 I [2] C2/m (12); [2] C2/c (15); [2] C2221 (20); [2] C222 (21); [2] F222 (22); [2] I222 (23); [2] I212121 (24); [2] Amm2 (38); [2] Aem2 (39); [2] Ama2 (40); [2] Aea2 (41); [2] Fmm2 (42); [2] Fdd2 (43); [2] Imm2 (44); [2] Iba2 (45); [2] Ima2 (46); [2] I4 (79); [2] I41 (80); [2] I-4 (82); [3] P312 (149); [3] P321 (150); [3] P3112 (151); [3] P3121 (152); [3] P3212 (153); [3] P3221 (154); [3] R32 (155)
 II [2] P112 (b' = 1/2b, c' = 1/2c) (P2, 3)

UNIQUE AXIS c, DIFFERENT CELL CHOICES

A112

UNIQUE AXIS c, CELL CHOICE 1

Origin on 2

 Asymmetric unit 0 ≤ x ≤ 1; 0 ≤ y ≤ 1/2; 0 ≤ z ≤ 1/2

Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); t(0, 1/21/2); (2)

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
(0, 0, 0)+  (0, 1/21/2)+  General:
 4 c 1
 (1) x, y, z (2) -x, -y, z
hkl : k + l = 2n
hk0 : k = 2n
0kl : k + l = 2n
h0l : l = 2n
00l : l = 2n
0k0 : k = 2n
Special: as above, plus
 2 b 2
 1/2, 0, z
no extra conditions
 2 a 2
 0, 0, z
no extra conditions

B112

UNIQUE AXIS c, CELL CHOICE 2

Origin on 2

 Asymmetric unit 0 ≤ x ≤ 1; 0 ≤ y ≤ 1/2; 0 ≤ z ≤ 1/2

Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); t(1/2, 0, 1/2); (2)

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
(0, 0, 0)+  (1/2, 0, 1/2)+  General:
 4 c 1
 (1) x, y, z (2) -x, -y, z
hkl : h + l = 2n
hk0 : h = 2n
0kl : l = 2n
h0l : h + l = 2n
00l : l = 2n
h00 : h = 2n
Special: as above, plus
 2 b 2
 1/2, 1/2, z
no extra conditions
 2 a 2
 0, 0, z
no extra conditions

I112

UNIQUE AXIS c, CELL CHOICE 3

Origin on 2

 Asymmetric unit 0 ≤ x ≤ 1; 0 ≤ y ≤ 1/2; 0 ≤ z ≤ 1/2

Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); t(1/21/21/2); (2)

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
(0, 0, 0)+  (1/21/21/2)+  General:
 4 c 1
 (1) x, y, z (2) -x, -y, z
hkl : h + k + l = 2n
hk0 : h + k = 2n
0kl : k + l = 2n
h0l : h + l = 2n
00l : l = 2n
h00 : h = 2n
0k0 : k = 2n
Special: as above, plus
 2 b 2
 0, 1/2, z
no extra conditions
 2 a 2
 0, 0, z
no extra conditions