Pc Cs2 m Monoclinic No. 7 P1c1 Patterson symmetry P12/m1 UNIQUE AXIS b, CELL CHOICE 1

Origin on glide plane c

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

Symmetry operations

 (1)  1 (2)  c   x, 0, z

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
General:
 2 a 1
 (1) x, y, z (2) x, -y, z + 1/2
h0l : l = 2n
00l : l = 2n

Symmetry of special projections

 Along [001]   p11ma' = ap   b' = b   Origin at 0, 0, z Along [100]   p1g1a' = b   b' = cp   Origin at x, 0, 0 Along [010]   p1a' = 1/2c   b' = a   Origin at 0, y, 0

Maximal non-isomorphic subgroups

 I [2] P1 (1) 1
 IIa none
 IIb [2] C1c1 (a' = 2a, b' = 2b) (Cc, 9)

Maximal isomorphic subgroups of lowest index

 IIc [2] P1c1 (b' = 2b) (Pc, 7); [2] P1c1 (a' = 2a or a' = 2a, c' = 2a + c) (Pc, 7)

Minimal non-isomorphic supergroups

 I [2] P2/c (13); [2] P21/c (14); [2] Pmc21 (26); [2] Pcc2 (27); [2] Pma2 (28); [2] Pca21 (29); [2] Pnc2 (30); [2] Pmn21 (31); [2] Pba2 (32); [2] Pna21 (33); [2] Pnn2 (34); [2] Aem2 (39); [2] Aea2 (41)
 II [2] C1c1 (Cc, 9); [2] A1m1 (Cm, 8); [2] I1c1 (Cc, 9); [2] P1m1 (c' = 1/2c) (Pm, 6)

UNIQUE AXIS b, DIFFERENT CELL CHOICES

P1c1

UNIQUE AXIS b, CELL CHOICE 1

Origin on glide plane c

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

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
General:
 2 a 1
 (1) x, y, z (2) x, -y, z + 1/2
h0l : l = 2n
00l : l = 2n

P1n1

UNIQUE AXIS b, CELL CHOICE 2

Origin on glide plane n

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

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
General:
 2 a 1
 (1) x, y, z (2) x + 1/2, -y, z + 1/2
h0l : h + l = 2n
h00 : h = 2n
00l : l = 2n

P1a1

UNIQUE AXIS b, CELL CHOICE 3

Origin on glide plane a

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

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
General:
 2 a 1
 (1) x, y, z (2) x + 1/2, -y, z
h0l : h = 2n
h00 : h = 2n

 Pc Cs2 m Monoclinic No. 7 P11a Patterson symmetry P112/m UNIQUE AXIS c, CELL CHOICE 1

Origin on glide plane a

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

Symmetry operations

 (1)  1 (2)  a   x, y, 0

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
General:
 2 a 1
 (1) x, y, z (2) x + 1/2, y, -z
hk0 : h = 2n
h00 : h = 2n

Symmetry of special projections

 Along [001]   p1a' = 1/2a   b' = b   Origin at 0, 0, z Along [100]   p11ma' = bp   b' = c   Origin at x, 0, 0 Along [010]   p1g1a' = c   b' = ap   Origin at 0, y, 0

Maximal non-isomorphic subgroups

 I [2] P1 (1) 1
 IIa none
 IIb [2] A11a (b' = 2b, c' = 2c) (Cc, 9)

Maximal isomorphic subgroups of lowest index

 IIc [2] P11a (c' = 2c) (Pc, 7); [2] P11a (b' = 2b or a' = a + 2b, b' = 2b) (Pc, 7)

Minimal non-isomorphic supergroups

 I [2] P2/c (13); [2] P21/c (14); [2] Pmc21 (26); [2] Pcc2 (27); [2] Pma2 (28); [2] Pca21 (29); [2] Pnc2 (30); [2] Pmn21 (31); [2] Pba2 (32); [2] Pna21 (33); [2] Pnn2 (34); [2] Aem2 (39); [2] Aea2 (41)
 II [2] A11a (Cc, 9); [2] B11m (Cm, 8); [2] I11a (Cc, 9); [2] P11m (a' = 1/2a) (Pm, 6)

UNIQUE AXIS c, DIFFERENT CELL CHOICES

P11a

UNIQUE AXIS c, CELL CHOICE 1

Origin on glide plane a

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

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
General:
 2 a 1
 (1) x, y, z (2) x + 1/2, y, -z
hk0 : h = 2n
h00 : h = 2n

P11n

UNIQUE AXIS c, CELL CHOICE 2

Origin on glide plane n

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

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
General:
 2 a 1
 (1) x, y, z (2) x + 1/2, y + 1/2, -z
hk0 : h + k = 2n
h00 : h = 2n
0k0 : k = 2n

P11b

UNIQUE AXIS c, CELL CHOICE 3

Origin on glide plane b

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

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
General:
 2 a 1
 (1) x, y, z (2) x, y + 1/2, -z
hk0 : k = 2n
0k0 : k = 2n