Cc Cs4 m Monoclinic info
No. 9 C1c1 Patterson symmetry C12/m1
UNIQUE AXIS b, CELL CHOICE 1

symmetry group diagram

Origin on glide plane c

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

Symmetry operations

For (0, 0, 0)+ set

(1)  1   (2)  c   x, 0, z

For (1/21/2, 0)+ set

(1)  t(1/21/2, 0)   (2)  n(1/2, 0, 1/2)   x1/4z

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 a 1
(1) xyz(2) x-yz + 1/2
hkl : h + k = 2n
h0l : hl = 2n
0kl : k = 2n
hk0 : h + k = 2n
0k0 : k = 2n
h00 : h = 2n
00l : l = 2n

Symmetry of special projections

Along [001]   c11m
a' = ap   b' = b   
Origin at 0, 0, z
Along [100]   p1g1
a' = 1/2b   b' = cp   
Origin at x, 0, 0
Along [010]   p1
a' = 1/2c   b' = 1/2a   
Origin at 0, y, 0

Maximal non-isomorphic subgroups

I [2] C1 (P1, 1)1+
IIa [2] P1c1 (Pc, 7)1; 2
  [2] P1n1 (Pc, 7)1; 2 + (1/21/2, 0)
IIbnone

Maximal isomorphic subgroups of lowest index

IIc[3] C1c1 (b' = 3b) (Cc, 9); [3] C1c1 (c' = 3c) (Cc, 9); [3] C1c1 (a' = 3a or a' = 3ac' = -a + c or a' = 3ac' = a + c) (Cc, 9)

Minimal non-isomorphic supergroups

I[2] C2/c (15); [2] Cmc21 (36); [2] Ccc2 (37); [2] Ama2 (40); [2] Aea2 (41); [2] Fdd2 (43); [2] Iba2 (45); [2] Ima2 (46); [3] P3c1 (158); [3] P31c (159); [3] R3c (161)
II[2] F1m1 (Cm, 8); [2] C1m1 (c' = 1/2c) (Cm, 8); [2] P1c1 (a' = 1/2a, b' = 1/2b) (Pc, 7)

UNIQUE AXIS b, DIFFERENT CELL CHOICES

symmetry group diagram

C1c1

UNIQUE AXIS b, CELL CHOICE 1

cell choice

Origin on glide plane c

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 a 1
(1) xyz(2) x-yz + 1/2
hkl : h + k = 2n
h0l : hl = 2n
0kl : k = 2n
hk0 : h + k = 2n
0k0 : k = 2n
h00 : h = 2n
00l : l = 2n

A1n1

UNIQUE AXIS b, CELL CHOICE 2

cell choice

Origin on glide plane n

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 a 1
(1) xyz(2) x + 1/2-yz + 1/2
hkl : k + l = 2n
h0l : hl = 2n
0kl : k + l = 2n
hk0 : k = 2n
0k0 : k = 2n
h00 : h = 2n
00l : l = 2n

I1a1

UNIQUE AXIS b, CELL CHOICE 3

cell choice

Origin on glide plane a

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 a 1
(1) xyz(2) x + 1/2-yz
hkl : h + k + l = 2n
h0l : hl = 2n
0kl : k + l = 2n
hk0 : h + k = 2n
0k0 : k = 2n
h00 : h = 2n
00l : l = 2n





Cc Cs4 m Monoclinic info
No. 9 A11a Patterson symmetry A112/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 ≤ 1/4

Symmetry operations

For (0,  0,  0)+ set

(1)  1   (2)  a   xy, 0

For (0, 1/21/2)+ set

(1)  t(0, 1/21/2)   (2)  n(1/21/2, 0)   xy1/4

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 a 1
(1) xyz(2) x + 1/2y-z
hkl : k + l = 2n
hk0 : hk = 2n
0kl : k + l = 2n
h0l : l = 2n
00l : l = 2n
h00 : h = 2n
0k0 : k = 2n

Symmetry of special projections

Along [001]   p1
a' = 1/2a   b' = 1/2b   
Origin at 0, 0, z
Along [100]   c11m
a' = bp   b' = c   
Origin at x, 0, 0
Along [010]   p1g1
a' = 1/2c   b' = ap   
Origin at 0, y, 0

Maximal non-isomorphic subgroups

I [2] A1 (P1, 1)1+
IIa [2] P11a (Pc, 7)1; 2
  [2] P11n (Pc, 7)1; 2 + (0, 1/21/2)
IIbnone

Maximal isomorphic subgroups of lowest index

IIc[3] A11a (c' = 3c) (Cc, 9); [3] A11a (a' = 3a) (Cc, 9); [3] A11a (b' = 3b or a' = a - bb' = 3b or a' = a + bb' = 3b) (Cc, 9)

Minimal non-isomorphic supergroups

I[2] C2/c (15); [2] Cmc21 (36); [2] Ccc2 (37); [2] Ama2 (40); [2] Aea2 (41); [2] Fdd2 (43); [2] Iba2 (45); [2] Ima2 (46); [3] P3c1 (158); [3] P31c (159); [3] R3c (161)
II[2] F11m (Cm, 8); [2] A11m (a' = 1/2a) (Cm, 8); [2] P11a (b' = 1/2b, c' = 1/2c) (Pc, 7)

UNIQUE AXIS c, DIFFERENT CELL CHOICES

symmetry group diagram

A11a

UNIQUE AXIS c, CELL CHOICE 1

cell choice

Origin on glide plane a

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 a 1
(1) xyz(2) x + 1/2y-z
hkl : k + l = 2n
hk0 : hk = 2n
0kl : k + l = 2n
h0l : l = 2n
00l : l = 2n
h00 : h = 2n
0k0 : k = 2n

B11n

UNIQUE AXIS c, CELL CHOICE 2

cell choice

Origin on glide plane n

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 a 1
(1) xyz(2) x + 1/2y + 1/2-z
hkl : h + l = 2n
hk0 : hk = 2n
0kl : l = 2n
h0l : h + l = 2n
00l : l = 2n
h00 : h = 2n
0k0 : k = 2n

I11b

UNIQUE AXIS c, CELL CHOICE 3

cell choice

Origin on glide plane b

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 a 1
(1) xyz(2) xy + 1/2-z
hkl : h + k + l = 2n
hk0 : hk = 2n
0kl : k + l = 2n
h0l : h + l = 2n
00l : l = 2n
h00 : h = 2n
0k0 : k = 2n








































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