Cm Cs3 m Monoclinic No. 8 C1m1 Patterson symmetry C12/m1 UNIQUE AXIS b, CELL CHOICE 1

Origin on mirror plane m

 Asymmetric unit 0 ≤ x ≤ 1; 0 ≤ y ≤ 1/4; 0 ≤ z ≤ 1

Symmetry operations

For (0, 0, 0)+ set

 (1)  1 (2)  m   x, 0, z

For (1/21/2, 0)+ set

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

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 b 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 a m
 x, 0, z
no extra conditions

Symmetry of special projections

 Along [001]   c11ma' = ap   b' = b   Origin at 0, 0, z Along [100]   p1m1a' = 1/2b   b' = cp   Origin at x, 0, 0 Along [010]   p1a' = c   b' = 1/2a   Origin at 0, y, 0

Maximal non-isomorphic subgroups

 I [2] C1 (P1, 1) 1+
 IIa [2] P1a1 (Pc, 7) 1; 2 + (1/2, 1/2, 0) [2] P1m1 (Pm, 6) 1; 2
 IIb [2] C1c1 (c' = 2c) (Cc, 9); [2] I1c1 (c' = 2c) (Cc, 9)

Maximal isomorphic subgroups of lowest index

 IIc [2] C1m1 (c' = 2c or a' = a + 2c, c' = 2c) (Cm, 8); [3] C1m1 (b' = 3b) (Cm, 8)

Minimal non-isomorphic supergroups

 I [2] C2/m (12); [2] Cmm2 (35); [2] Cmc21 (36); [2] Amm2 (38); [2] Aem2 (39); [2] Fmm2 (42); [2] Imm2 (44); [2] Ima2 (46); [3] P3m1 (156); [3] P31m (157); [3] R3m (160)
 II [2] P1m1 (a' = 1/2a, b' = 1/2b) (Pm, 6)

UNIQUE AXIS b, DIFFERENT CELL CHOICES

C1m1

UNIQUE AXIS b, CELL CHOICE 1

Origin on mirror plane m

 Asymmetric unit 0 ≤ x ≤ 1; 0 ≤ y ≤ 1/4; 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 b 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 a m
 x, 0, z
no extra conditions

A1m1

UNIQUE AXIS b, CELL CHOICE 2

Origin on mirror plane m

 Asymmetric unit 0 ≤ x ≤ 1; 0 ≤ y ≤ 1/4; 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 b 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 a m
 x, 0, z
no extra conditions

I1m1

UNIQUE AXIS b, CELL CHOICE 3

Origin on mirror plane m

 Asymmetric unit 0 ≤ x ≤ 1; 0 ≤ y ≤ 1/4; 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 b 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 a m
 x, 0, z
no extra conditions

 Cm Cs3 m Monoclinic No. 8 A11m Patterson symmetry A112/m UNIQUE AXIS c, CELL CHOICE 1

Origin on mirror plane m

 Asymmetric unit 0 ≤ x ≤ 1; 0 ≤ y ≤ 1; 0 ≤ z ≤ 1/4

Symmetry operations

For (0,  0,  0)+ set

 (1)  1 (2)  m   x, y, 0

For (0, 1/21/2)+ set

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

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 b 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 a m
 x, y, 0
no extra conditions

Symmetry of special projections

 Along [001]   p1a' = a   b' = 1/2b   Origin at 0, 0, z Along [100]   c11ma' = bp   b' = c   Origin at x, 0, 0 Along [010]   p1m1a' = 1/2c   b' = ap   Origin at 0, y, 0

Maximal non-isomorphic subgroups

 I [2] A1 (P1, 1) 1+
 IIa [2] P11b (Pc, 7) 1; 2 + (0, 1/2, 1/2) [2] P11m (Pm, 6) 1; 2
 IIb [2] A11a (a' = 2a) (Cc, 9); [2] I11a (a' = 2a) (Cc, 9)

Maximal isomorphic subgroups of lowest index

 IIc [2] A11m (a' = 2a or a' = 2a, b' = 2a + b) (Cm, 8); [3] A11m (c' = 3c) (Cm, 8)

Minimal non-isomorphic supergroups

 I [2] C2/m (12); [2] Cmm2 (35); [2] Cmc21 (36); [2] Amm2 (38); [2] Aem2 (39); [2] Fmm2 (42); [2] Imm2 (44); [2] Ima2 (46); [3] P3m1 (156); [3] P31m (157); [3] R3m (160)
 II [2] P11m (b' = 1/2b, c' = 1/2c) (Pm, 6)

UNIQUE AXIS c, DIFFERENT CELL CHOICES

A11m

UNIQUE AXIS c, CELL CHOICE 1

Origin on mirror plane m

 Asymmetric unit 0 ≤ x ≤ 1; 0 ≤ y ≤ 1; 0 ≤ z ≤ 1/4

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 b 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 a m
 x, y, 0
no extra conditions

B11m

UNIQUE AXIS c, CELL CHOICE 2

Origin on mirror plane m

 Asymmetric unit 0 ≤ x ≤ 1; 0 ≤ y ≤ 1; 0 ≤ z ≤ 1/4

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 b 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 a m
 x, y, 0
no extra conditions

I11m

UNIQUE AXIS c, CELL CHOICE 3

Origin on mirror plane m

 Asymmetric unit 0 ≤ x ≤ 1; 0 ≤ y ≤ 1; 0 ≤ z ≤ 1/4

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 b 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 a m
 x, y, 0
no extra conditions