Amm2 C2v14 mm2 Orthorhombic info
No. 38 Amm2 Patterson symmetry Ammm (Cmmm)

symmetry group diagram

Origin on m m 2

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, 0, z(3)  m   x, 0, z(4)  m   0, yz

For (0, 1/21/2)+ set

(1)  t(0, 1/21/2)   (2)  2(0, 0, 1/2)   0, 1/4z(3)  c   x1/4z(4)  n(0, 1/21/2)   0, yz

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-yz(3) x-yz(4) -xyz
hkl : k + l = 2n
0kl : k + l = 2n
h0l : l = 2n
hk0 : k = 2n
0k0 : k = 2n
00l : l = 2n
    Special: as above, plus
4 e  m . . 
1/2yz 1/2-yz
no extra conditions
4 d  m . . 
0, yz 0, -yz
no extra conditions
4 c  . m . 
x, 0, z -x, 0, z
no extra conditions
2 b  m m 2 
1/2, 0, z
no extra conditions
2 a  m m 2 
0, 0, z
no extra conditions

Symmetry of special projections

Along [001]   p2mm
a' = a   b' = 1/2b   
Origin at 0, 0, z
Along [100]   c1m1
a' = b   b' = c   
Origin at x, 0, 0
Along [010]   p11m
a' = 1/2c   b' = a   
Origin at 0, y, 0

Maximal non-isomorphic subgroups

I [2] A1m1 (Cm, 8)(1; 3)+
  [2] Am11 (Pm, 6)(1; 4)+
  [2] A112 (C2, 5)(1; 2)+
IIa [2] Pnm21 (Pmn21, 31)1; 3; (2; 4) + (0, 1/21/2)
  [2] Pnc2 (30)1; 2; (3; 4) + (0, 1/21/2)
  [2] Pmc21 (26)1; 4; (2; 3) + (0, 1/21/2)
  [2] Pmm2 (25)1; 2; 3; 4
IIb[2] Ima2 (a' = 2a) (46); [2] Imm2 (a' = 2a) (44); [2] Ama2 (a' = 2a) (40)

Maximal isomorphic subgroups of lowest index

IIc[2] Amm2 (a' = 2a) (38); [3] Amm2 (b' = 3b) (38); [3] Amm2 (c' = 3c) (38)

Minimal non-isomorphic supergroups

I[2] Cmcm (63); [2] Cmmm (65); [3] P-6m2 (187); [3] P-62m (189)
II[2] Fmm2 (42); [2] Pmm2 (b' = 1/2b, c' = 1/2c) (25)








































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