C2/c C2h6 2/m Monoclinic info
No. 15 C12/c1 Patterson symmetry C12/m1
UNIQUE AXIS b, CELL CHOICE 1

symmetry group diagram

Origin at -1 on glide plane c

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

Symmetry operations

For (0, 0, 0)+ set

(1)  1   (2)  2   0, y1/4(3)  -1   0, 0, 0(4)  c   x, 0, z

For (1/21/2, 0)+ set

(1)  t(1/21/2, 0)   (2)  2(0, 1/2, 0)   1/4y1/4(3)  -1   1/41/4, 0(4)  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); (3)

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
 (0, 0, 0)+  (1/21/2, 0)+  General:
8 f 1
(1) xyz(2) -xy-z + 1/2(3) -x-y-z(4) 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
    Special: as above, plus
4 e  2 
0, y1/4 0, -y3/4
no extra conditions
4 d  -1 
1/41/41/2 3/41/4, 0
hkl: k  +  l  =  2n
4 c  -1 
1/41/4, 0 3/41/41/2
hkl: k  +  l  =  2n
4 b  -1 
0, 1/2, 0 0, 1/21/2
hkl: l  =  2n
4 a  -1 
0, 0, 0 0, 0, 1/2
hkl: l  =  2n

Symmetry of special projections

Along [001]   c2mm
a' = ap   b' = b   
Origin at 0, 0, z
Along [100]   p2gm
a' = 1/2b   b' = cp   
Origin at x, 0, 0
Along [010]   p2
a' = 1/2c   b' = 1/2a   
Origin at 0, y, 0

UNIQUE AXIS b, DIFFERENT CELL CHOICES

symmetry group diagram

C12/c1

UNIQUE AXIS b, CELL CHOICE 1

cell choice

Origin at -1 on glide plane c

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

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
 (0, 0, 0)+  (1/21/2, 0)+  General:
8 f 1
(1) xyz(2) -xy-z + 1/2(3) -x-y-z(4) 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
    Special: as above, plus
4 e  2 
0, y1/4 0, -y3/4
no extra conditions
4 d  -1 
1/41/41/2 3/41/4, 0
hkl: k + l = 2n
4 c  -1 
1/41/4, 0 3/41/41/2
4 b  -1 
0, 1/2, 0 0, 1/21/2
hkl: l = 2n
4 a  -1 
0, 0, 0 0, 0, 1/2

A12/n1

UNIQUE AXIS b, CELL CHOICE 2

cell choice

Origin at -1 on glide plane n

Asymmetric unit 0 ≤ x ≤ 1/2; 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); (3)

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
 (0, 0, 0)+  (0, 1/21/2)+  General:
8 f 1
(1) xyz(2) -x + 1/2y-z + 1/2(3) -x-y-z(4) 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
    Special: as above, plus
4 e  2 
3/4y3/4 1/4-y1/4
no extra conditions
4 d  -1 
1/21/43/4 0, 1/43/4
hkl: h = 2n
4 c  -1 
0, 1/41/4 1/21/41/4
4 b  -1 
0, 1/2, 0 1/21/21/2
hkl: h + k = 2n
4 a  -1 
0, 0, 0 1/2, 0, 1/2

I12/a1

UNIQUE AXIS b, CELL CHOICE 3

cell choice

Origin at -1 on glide plane a

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 f 1
(1) xyz(2) -x + 1/2y-z(3) -x-y-z(4) 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
    Special: as above, plus
4 e  2 
1/4y, 0 3/4-y, 0
no extra conditions
4 d  -1 
1/41/43/4 1/41/41/4
hkl: l = 2n
4 c  -1 
3/41/43/4 3/41/41/4
4 b  -1 
0, 1/2, 0 1/21/2, 0
hkl: h = 2n
4 a  -1 
0, 0, 0 1/2, 0, 0





C2/c C2h6 2/m Monoclinic info
No. 15 A112/a Patterson symmetry A112/m
UNIQUE AXIS c, CELL CHOICE 1

symmetry group diagram

Origin at -1 on glide plane a

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

Symmetry operations

For (0,  0,  0)+ set

(1)  1   (2)  2   1/4, 0, z(3)  -1   0, 0, 0(4)  a   xy, 0

For (0, 1/21/2)+ set

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

Positions

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

Symmetry of special projections

Along [001]   p2
a' = 1/2a   b' = 1/2b   
Origin at 0, 0, z
Along [100]   c2mm
a' = bp   b' = c   
Origin at x, 0, 0
Along [010]   p2gm
a' = 1/2c   b' = ap   
Origin at 0, y, 0

UNIQUE AXIS c, DIFFERENT CELL CHOICES

symmetry group diagram

A112/a

UNIQUE AXIS c, CELL CHOICE 1

cell choice

Origin at -1 on glide plane a

Asymmetric unit 0 ≤ x ≤ 1/2; 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); (3)

Positions

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

B112/n

UNIQUE AXIS c, CELL CHOICE 2

cell choice

Origin at -1 on glide plane n

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

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 f 1
(1) xyz(2) -x + 1/2-y + 1/2z(3) -x-y-z(4) 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
    Special: as above, plus
4 e  2 
3/43/4z 1/41/4-z
no extra conditions
4 d  -1 
3/41/21/4 3/4, 0, 1/4
hkl: k = 2n
4 c  -1 
1/4, 0, 1/4 1/41/21/4
4 b  -1 
0, 0, 1/2 1/21/21/2
hkl: h + k = 2n
4 a  -1 
0, 0, 0 1/21/2, 0

I112/b

UNIQUE AXIS c, CELL CHOICE 3

cell choice

Origin at -1 on glide plane b

Asymmetric unit 0 ≤ x ≤ 1/4; 0 ≤ y ≤ 1; 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); (3)

Positions

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








































to end of page
to top of page