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

symmetry group diagram

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) xyz(2) x-yz + 1/2
h0l : l = 2n
00l : l = 2n

Symmetry of special projections

Along [001]   p11m
a' = ap   b' = b   
Origin at 0, 0, z
Along [100]   p1g1
a' = b   b' = cp   
Origin at x, 0, 0
Along [010]   p1
a' = 1/2c   b' = a   
Origin at 0, y, 0

Maximal non-isomorphic subgroups

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

Maximal isomorphic subgroups of lowest index

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

symmetry group diagram

P1c1

UNIQUE AXIS b, CELL CHOICE 1

cell choice

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) xyz(2) x-yz + 1/2
h0l : l = 2n
00l : l = 2n

P1n1

UNIQUE AXIS b, CELL CHOICE 2

cell choice

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) xyz(2) x + 1/2-yz + 1/2
h0l : h + l = 2n
h00 : h = 2n
00l : l = 2n

P1a1

UNIQUE AXIS b, CELL CHOICE 3

cell choice

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) xyz(2) x + 1/2-yz
h0l : h = 2n
h00 : h = 2n





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

symmetry group diagram

Origin on glide plane a

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

Symmetry operations

(1)  1   (2)  a   xy, 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) xyz(2) x + 1/2y-z
hk0 : h = 2n
h00 : h = 2n

Symmetry of special projections

Along [001]   p1
a' = 1/2a   b' = b   
Origin at 0, 0, z
Along [100]   p11m
a' = bp   b' = c   
Origin at x, 0, 0
Along [010]   p1g1
a' = c   b' = ap   
Origin at 0, y, 0

Maximal non-isomorphic subgroups

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

Maximal isomorphic subgroups of lowest index

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

symmetry group diagram

P11a

UNIQUE AXIS c, CELL CHOICE 1

cell choice

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) xyz(2) x + 1/2y-z
hk0 : h = 2n
h00 : h = 2n

P11n

UNIQUE AXIS c, CELL CHOICE 2

cell choice

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) xyz(2) x + 1/2y + 1/2-z
hk0 : h + k = 2n
h00 : h = 2n
0k0 : k = 2n

P11b

UNIQUE AXIS c, CELL CHOICE 3

cell choice

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) xyz(2) xy + 1/2-z
hk0 : k = 2n
0k0 : k = 2n








































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