C2/m C2h3 2/m Monoclinic info
No. 12 C12/m1 Patterson symmetry C12/m1
UNIQUE AXIS b, CELL CHOICE 1

symmetry group diagram

Origin at centre (2/m)

Asymmetric unit 0 ≤ x ≤ 1/2; 0 ≤ y ≤ 1/4; 0 ≤ z ≤ 1

Symmetry operations

For (0, 0, 0)+ set

(1)  1   (2)  2   0, y, 0(3)  -1   0, 0, 0(4)  m   x, 0, z

For (1/21/2, 0)+ set

(1)  t(1/21/2, 0)   (2)  2(0, 1/2, 0)   1/4y, 0(3)  -1   1/41/4, 0(4)  a   x1/4z

Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); t(1/21/2, 0); (2); (3)

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
 (0, 0, 0)+  (1/21/2, 0)+  General:
8 j 1
(1) xyz(2) -xy-z(3) -x-y-z(4) x-yz
hkl: h + k = 2n
h0l: h = 2n
0kl: k = 2n
hk0: h + k = 2n
0k0: k = 2n
h00: h = 2n
    Special: as above, plus
4 i  m 
x, 0, z -x, 0, -z
no extra conditions
4 h  2 
0, y1/2 0, -y1/2
no extra conditions
4 g  2 
0, y, 0 0, -y, 0
no extra conditions
4 f  -1 
1/41/41/2 3/41/41/2
hkl: h  =  2n
4 e  -1 
1/41/4, 0 3/41/4, 0
hkl: h  =  2n
2 d  2/m 
0, 1/21/2
no extra conditions
2 c  2/m 
0, 0, 1/2
no extra conditions
2 b  2/m 
0, 1/2, 0
no extra conditions
2 a  2/m 
0, 0, 0
no extra conditions

Symmetry of special projections

Along [001]   c2mm
a' = ap   b' = b   
Origin at 0, 0, z
Along [100]   p2mm
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

C12/m1

UNIQUE AXIS b, CELL CHOICE 1

cell choice

Origin at centre (2/m)

Asymmetric unit 0 ≤ x ≤ 1/2; 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); (3)

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
 (0, 0, 0)+  (1/21/2, 0)+  General:
8 j 1
(1) xyz(2) -xy-z(3) -x-y-z(4) x-yz
hkl: h + k = 2n
h0l: h = 2n
0kl: k = 2n
hk0: h + k = 2n
0k0: k = 2n
h00: h = 2n
    Special: as above, plus
4 i  m 
x, 0, z -x, 0, -z
no extra conditions
4 h  2 
0, y1/2 0, -y1/2
no extra conditions
4 g  2 
0, y, 0 0, -y, 0
4 f  -1 
1/41/41/2 3/41/41/2
hkl: h = 2n
4 e  -1 
1/41/4, 0 3/41/4, 0
2 d  2/m 
0, 1/21/2
no extra conditions
2 c  2/m 
0, 0, 1/2
2 b  2/m 
0, 1/2, 0
no extra conditions
2 a  2/m 
0, 0, 0

A12/m1

UNIQUE AXIS b, CELL CHOICE 2

cell choice

Origin at centre (2/m)

Asymmetric unit 0 ≤ x ≤ 1/2; 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); (3)

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
 (0, 0, 0)+  (0, 1/21/2)+  General:
8 j 1
(1) xyz(2) -xy-z(3) -x-y-z(4) x-yz
hkl: k + l = 2n
h0l: l = 2n
0kl: k + l = 2n
hk0: k = 2n
0k0: k = 2n
00l: l = 2n
    Special: as above, plus
4 i  m 
x, 0, z -x, 0, -z
no extra conditions
4 h  2 
1/2y1/2 1/2-y1/2
no extra conditions
4 g  2 
0, y, 0 0, -y, 0
4 f  -1 
1/21/43/4 1/21/41/4
hkl: k = 2n
4 e  -1 
0, 1/41/4 0, 1/43/4
2 d  2/m 
1/21/21/2
no extra conditions
2 c  2/m 
1/2, 0, 1/2
2 b  2/m 
0, 1/2, 0
no extra conditions
2 a  2/m 
0, 0, 0

I12/m1

UNIQUE AXIS b, CELL CHOICE 3

cell choice

Origin at centre (2/m)

Asymmetric unit 0 ≤ x ≤ 1/2; 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); (3)

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
 (0, 0, 0)+  (1/21/21/2)+  General:
8 j 1
(1) xyz(2) -xy-z(3) -x-y-z(4) x-yz
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
4 i  m 
x, 0, z -x, 0, -z
no extra conditions
4 h  2 
1/2y, 0 1/2-y, 0
no extra conditions
4 g  2 
0, y, 0 0, -y, 0
4 f  -1 
1/41/43/4 3/41/41/4
hkl: k = 2n
4 e  -1 
3/41/43/4 1/41/41/4
2 d  2/m 
1/21/2, 0
no extra conditions
2 c  2/m 
1/2, 0, 0
2 b  2/m 
0, 1/2, 0
no extra conditions
2 a  2/m 
0, 0, 0





C2/m C2h3 2/m Monoclinic info
No. 12 A112/m Patterson symmetry A112/m
UNIQUE AXIS c, CELL CHOICE 1

symmetry group diagram

Origin at centre (2/m)

Asymmetric unit 0 ≤ x ≤ 1; 0 ≤ y ≤ 1/2; 0 ≤ z ≤ 1/4

Symmetry operations

For (0,  0,  0)+ set

(1)  1   (2)  2   0, 0, z(3)  -1   0, 0, 0(4)  m   xy, 0

For (0, 1/21/2)+ set

(1)  t(0, 1/21/2)   (2)  2(0, 0, 1/2)   0, 1/4z(3)  -1   0, 1/41/4(4)  b   xy1/4

Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); t(0, 1/21/2); (2); (3)

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
 (0, 0, 0)+  (0, 1/21/2)+  General:
8 j 1
(1) xyz(2) -x-yz(3) -x-y-z(4) xy-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
4 i  m 
xy, 0 -x-y, 0
no extra conditions
4 h  2 
1/2, 0, z 1/2, 0, -z
no extra conditions
4 g  2 
0, 0, z 0, 0, -z
no extra conditions
4 f  -1 
1/21/41/4 1/23/41/4
hkl: k  =  2n
4 e  -1 
0, 1/41/4 0, 3/41/4
hkl: k  =  2n
2 d  2/m 
1/2, 0, 1/2
no extra conditions
2 c  2/m 
1/2, 0, 0
no extra conditions
2 b  2/m 
0, 0, 1/2
no extra conditions
2 a  2/m 
0, 0, 0
no extra conditions

Symmetry of special projections

Along [001]   p2
a' = a   b' = 1/2b   
Origin at 0, 0, z
Along [100]   c2mm
a' = bp   b' = c   
Origin at x, 0, 0
Along [010]   p2mm
a' = 1/2c   b' = ap   
Origin at 0, y, 0

UNIQUE AXIS c, DIFFERENT CELL CHOICES

symmetry group diagram

A112/m

UNIQUE AXIS c, CELL CHOICE 1

cell choice

Origin at centre (2/m)

Asymmetric unit 0 ≤ x ≤ 1; 0 ≤ y ≤ 1/2; 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); (3)

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
 (0, 0, 0)+  (0, 1/21/2)+  General:
8 j 1
(1) xyz(2) -x-yz(3) -x-y-z(4) xy-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
4 i  m 
xy, 0 -x-y, 0
no extra conditions
4 h  2 
1/2, 0, z 1/2, 0, -z
no extra conditions
4 g  2 
0, 0, z 0, 0, -z
4 f  -1 
1/21/41/4 1/23/41/4
hkl: k = 2n
4 e  -1 
0, 1/41/4 0, 3/41/4
2 d  2/m 
1/2, 0, 1/2
no extra conditions
2 c  2/m 
1/2, 0, 0
2 b  2/m 
0, 0, 1/2
no extra conditions
2 a  2/m 
0, 0, 0

B112/m

UNIQUE AXIS c, CELL CHOICE 2

cell choice

Origin at centre (2/m)

Asymmetric unit 0 ≤ x ≤ 1; 0 ≤ y ≤ 1/2; 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); (3)

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
 (0, 0, 0)+  (1/2, 0, 1/2)+  General:
8 j 1
(1) xyz(2) -x-yz(3) -x-y-z(4) xy-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
4 i  m 
xy, 0 -x-y, 0
no extra conditions
4 h  2 
1/21/2z 1/21/2-z
no extra conditions
4 g  2 
0, 0, z 0, 0, -z
4 f  -1 
3/41/21/4 1/41/21/4
hkl: h = 2n
4 e  -1 
1/4, 0, 1/4 3/4, 0, 1/4
2 d  2/m 
1/21/21/2
no extra conditions
2 c  2/m 
1/21/2, 0
2 b  2/m 
0, 0, 1/2
no extra conditions
2 a  2/m 
0, 0, 0

I112/m

UNIQUE AXIS c, CELL CHOICE 3

cell choice

Origin at centre (2/m)

Asymmetric unit 0 ≤ x ≤ 1; 0 ≤ y ≤ 1/2; 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); (3)

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
 (0, 0, 0)+  (1/21/21/2)+  General:
8 j 1
(1) xyz(2) -x-yz(3) -x-y-z(4) xy-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
4 i  m 
xy, 0 -x-y, 0
no extra conditions
4 h  2 
0, 1/2z 0, 1/2-z
no extra conditions
4 g  2 
0, 0, z 0, 0, -z
4 f  -1 
3/41/41/4 1/43/41/4
hkl: l = 2n
4 e  -1 
3/43/41/4 1/41/41/4
2 d  2/m 
0, 1/21/2
no extra conditions
2 c  2/m 
0, 1/2, 0
2 b  2/m 
0, 0, 1/2
no extra conditions
2 a  2/m 
0, 0, 0








































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