P21/m C2h2 2/m Monoclinic info
No. 11 P121/m1 Patterson symmetry P12/m1
UNIQUE AXIS b

symmetry group diagram

Origin at -1 on 21

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

Symmetry operations

(1)  1   (2)  2(0, 1/2, 0)   0, y, 0(3)  -1   0, 0, 0(4)  m   x1/4z

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
 General:
4 f 1
(1) xyz(2) -xy + 1/2-z(3) -x-y-z(4) x-y + 1/2z
0k0 : k = 2n
    Special: as above, plus
2 e  m 
x1/4z -x3/4-z
no extra conditions
2 d  -1 
1/2, 0, 1/2 1/21/21/2
hkl : k = 2n
2 c  -1 
0, 0, 1/2 0, 1/21/2
hkl : k = 2n
2 b  -1 
1/2, 0, 0 1/21/2, 0
hkl : k = 2n
2 a  -1 
0, 0, 0 0, 1/2, 0
hkl : k = 2n

Symmetry of special projections

Along [001]   p2gm
a' = ap   b' = b   
Origin at 0, 0, z
Along [100]   p2mg
a' = b   b' = cp   
Origin at x, 0, 0
Along [010]   p2
a' = c   b' = a   
Origin at 0, y, 0

Maximal non-isomorphic subgroups

I [2] P1m1 (Pm, 6)1; 4
  [2] P1211 (P21, 4)1; 2
  [2] P-1 (2)1; 3
IIa none
IIb[2] P121/c1 (c' = 2c) (P21/c, 14); [2] P121/a1 (a' = 2a) (P21/c, 14); [2] B121/e1 (a' = 2ac' = 2c) (P21/c, 14)

Maximal isomorphic subgroups of lowest index

IIc[2] P121/m1 (c' = 2c or a' = 2a or a' = a + cc' = -a + c) (P21/m, 11); [3] P121/m1 (b' = 3b) (P21/m, 11)

Minimal non-isomorphic supergroups

I[2] Pmma (51); [2] Pbcm (57); [2] Pmmn (59); [2] Pnma (62); [2] Cmcm (63); [3] P63/m (176)
II[2] C12/m1 (C2/m, 12); [2] A12/m1 (C2/m, 12); [2] I12/m1 (C2/m, 12); [2] P12/m1 (b' = 1/2b) (P2/m, 10)





P21/m C2h2 2/m Monoclinic info
No. 11 P1121/m Patterson symmetry P112/m
UNIQUE AXIS c

symmetry group diagram

Origin at -1 on 21

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

Symmetry operations

(1)  1   (2)  2(0, 0, 1/2)   0, 0, z(3)  -1   0, 0, 0(4)  m   xy1/4

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
 General:
4 f 1
(1) xyz(2) -x-yz + 1/2(3) -x-y-z(4) xy-z + 1/2
00l : l = 2n
    Special: as above, plus
2 e  m 
xy1/4 -x-y3/4
no extra conditions
2 d  -1 
1/21/2, 0 1/21/21/2
hkl : l = 2n
2 c  -1 
1/2, 0, 0 1/2, 0, 1/2
hkl : l = 2n
2 b  -1 
0, 1/2, 0 0, 1/21/2
hkl : l = 2n
2 a  -1 
0, 0, 0 0, 0, 1/2
hkl : l = 2n

Symmetry of special projections

Along [001]   p2
a' = a   b' = b   
Origin at 0, 0, z
Along [100]   p2gm
a' = bp   b' = c   
Origin at x, 0, 0
Along [010]   p2mg
a' = c   b' = ap   
Origin at 0, y, 0

Maximal non-isomorphic subgroups

I [2] P11m (Pm, 6)1; 4
  [2] P1121 (P21, 4)1; 2
  [2] P-1 (2)1; 3
IIa none
IIb[2] P1121/a (a' = 2a) (P21/c, 14); [2] P1121/b (b' = 2b) (P21/c, 14); [2] C1121/e (a' = 2ab' = 2b) (P21/c, 14)

Maximal isomorphic subgroups of lowest index

IIc[2] P1121/m (a' = 2a or b' = 2b or a' = a - bb' = a + b) (P21/m, 11); [3] P1121/m (c' = 3c) (P21/m, 11)

Minimal non-isomorphic supergroups

I[2] Pmma (51); [2] Pbcm (57); [2] Pmmn (59); [2] Pnma (62); [2] Cmcm (63); [3] P63/m (176)
II[2] A112/m (C2/m, 12); [2] B112/m (C2/m, 12); [2] I112/m (C2/m, 12); [2] P112/m (c' = 1/2c) (P2/m, 10)








































to end of page
to top of page