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

symmetry group diagram

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(1/21/2, 0)   (2)  2(0, 1/2, 0)   1/4y, 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) xyz(2) -xy-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, y1/2
no extra conditions
2 a  2 
0, y, 0
no extra conditions

Symmetry of special projections

Along [001]   c1m1
a' = ap   b' = b   
Origin at 0, 0, z
Along [100]   p11m
a' = 1/2b   b' = cp   
Origin at x, 0, 0
Along [010]   p2
a' = c   b' = 1/2a   
Origin at 0, y, 0

UNIQUE AXIS b, DIFFERENT CELL CHOICES

symmetry group diagram

C121

UNIQUE AXIS b, CELL CHOICE 1

cell choice

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) xyz(2) -xy-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, y1/2
no extra conditions
2 a  2 
0, y, 0
no extra conditions

A121

UNIQUE AXIS b, CELL CHOICE 2

cell choice

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) xyz(2) -xy-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 
1/2y1/2
no extra conditions
2 a  2 
0, y, 0
no extra conditions

I121

UNIQUE AXIS b, CELL CHOICE 3

cell choice

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) xyz(2) -xy-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 
1/2y, 0
no extra conditions
2 a  2 
0, y, 0
no extra conditions





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

symmetry group diagram

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, 1/21/2)   (2)  2(0, 0, 1/2)   0, 1/4z

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) xyz(2) -x-yz
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]   p2
a' = a   b' = 1/2b   
Origin at 0, 0, z
Along [100]   c1m1
a' = bp   b' = c   
Origin at x, 0, 0
Along [010]   p11m
a' = 1/2c   b' = ap   
Origin at 0, y, 0

UNIQUE AXIS c, DIFFERENT CELL CHOICES

symmetry group diagram

A112

UNIQUE AXIS c, CELL CHOICE 1

cell choice

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) xyz(2) -x-yz
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

cell choice

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) xyz(2) -x-yz
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 
1/21/2z
no extra conditions
2 a  2 
0, 0, z
no extra conditions

I112

UNIQUE AXIS c, CELL CHOICE 3

cell choice

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) xyz(2) -x-yz
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, 1/2z
no extra conditions
2 a  2 
0, 0, z
no extra conditions








































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