Cm Cs3 m Monoclinic info
No. 8 C1m1 Patterson symmetry C12/m1
UNIQUE AXIS b, CELL CHOICE 1

symmetry group diagram

Origin on mirror plane m

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

Symmetry operations

For (0, 0, 0)+ set

(1)  1   (2)  m   x, 0, z

For (1/21/2, 0)+ set

(1)  t(1/21/2, 0)   (2)  a   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 b 1
(1) xyz(2) 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
2 a  m 
x, 0, z
no extra conditions

Symmetry of special projections

Along [001]   c11m
a' = ap   b' = b   
Origin at 0, 0, z
Along [100]   p1m1
a' = 1/2b   b' = cp   
Origin at x, 0, 0
Along [010]   p1
a' = c   b' = 1/2a   
Origin at 0, y, 0

UNIQUE AXIS b, DIFFERENT CELL CHOICES

symmetry group diagram

C1m1

UNIQUE AXIS b, CELL CHOICE 1

cell choice

Origin on mirror plane m

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 b 1
(1) xyz(2) 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
2 a  m 
x, 0, z
no extra conditions

A1m1

UNIQUE AXIS b, CELL CHOICE 2

cell choice

Origin on mirror plane m

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 b 1
(1) xyz(2) 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
2 a  m 
x, 0, z
no extra conditions

I1m1

UNIQUE AXIS b, CELL CHOICE 3

cell choice

Origin on mirror plane m

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 b 1
(1) xyz(2) 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
2 a  m 
x, 0, z
no extra conditions





Cm Cs3 m Monoclinic info
No. 8 A11m Patterson symmetry A112/m
UNIQUE AXIS c, CELL CHOICE 1

symmetry group diagram

Origin on mirror plane m

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

Symmetry operations

For (0,  0,  0)+ set

(1)  1   (2)  m   xy, 0

For (0, 1/21/2)+ set

(1)  t(0, 1/21/2)   (2)  b   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 b 1
(1) xyz(2) 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
2 a  m 
xy, 0
no extra conditions

Symmetry of special projections

Along [001]   p1
a' = a   b' = 1/2b   
Origin at 0, 0, z
Along [100]   c11m
a' = bp   b' = c   
Origin at x, 0, 0
Along [010]   p1m1
a' = 1/2c   b' = ap   
Origin at 0, y, 0

UNIQUE AXIS c, DIFFERENT CELL CHOICES

symmetry group diagram

A11m

UNIQUE AXIS c, CELL CHOICE 1

cell choice

Origin on mirror plane m

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 b 1
(1) xyz(2) 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
2 a  m 
xy, 0
no extra conditions

B11m

UNIQUE AXIS c, CELL CHOICE 2

cell choice

Origin on mirror plane m

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 b 1
(1) xyz(2) 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
2 a  m 
xy, 0
no extra conditions

I11m

UNIQUE AXIS c, CELL CHOICE 3

cell choice

Origin on mirror plane m

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 b 1
(1) xyz(2) 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
2 a  m 
xy, 0
no extra conditions








































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