Cmc21 C2v12 mm2 Orthorhombic No. 36 Cmc21 Patterson symmetry Cmmm

Origin on m c 21

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

For (1/21/2, 0)+ set

 (1)  t(1/2, 1/2, 0) (2)  2(0, 0, 1/2)   1/4, 1/4, z (3)  n(1/2, 0, 1/2)   x, 1/4, z (4)  b   1/4, y, z

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 b 1
 (1) x, y, z (2) -x, -y, z + 1/2 (3) x, -y, z + 1/2 (4) -x, y, z
hkl : h + k = 2n
0kl : k = 2n
h0l : hl = 2n
hk0 : h + k = 2n
h00 : h = 2n
0k0 : k = 2n
00l : l = 2n
Special: as above, plus
 4 a m . .
 0, y, z 0, -y, z + 1/2
no extra conditions

Symmetry of special projections

 Along [001]   c2mma' = a   b' = b   Origin at 0, 0, z Along [100]   p1g1a' = 1/2b   b' = c   Origin at x, 0, 0 Along [010]   p11ma' = 1/2c   b' = 1/2a   Origin at 0, y, 0

Maximal non-isomorphic subgroups

 I [2] C1c1 (Cc, 9) (1; 3)+ [2] Cm11 (Cm, 8) (1; 4)+ [2] C1121 (P21, 4) (1; 2)+
 IIa [2] Pbn21 (Pna21, 33) 1; 2; (3; 4) + (1/2, 1/2, 0) [2] Pmn21 (31) 1; 4; (2; 3) + (1/2, 1/2, 0) [2] Pbc21 (Pca21, 29) 1; 3; (2; 4) + (1/2, 1/2, 0) [2] Pmc21 (26) 1; 2; 3; 4
 IIb none

Maximal isomorphic subgroups of lowest index

 IIc [3] Cmc21 (a' = 3a) (36); [3] Cmc21 (b' = 3b) (36); [3] Cmc21 (c' = 3c) (36)

Minimal non-isomorphic supergroups

 I [2] Cmcm (63); [2] Cmce (64); [3] P63cm (185); [3] P63mc (186)
 II [2] Fmm2 (42); [2] Pmc21 (a' = 1/2a, b' = 1/2b) (26); [2] Cmm2 (c' = 1/2c) (35)