[script p]4222 422 Tetragonal
No. 32 [script p]4222 Patterson symmetry [script p]4/mmm

symmetry group diagram

Origin at 222 at 4221

Asymmetric unit 0 ≤ x; 0 ≤ z ≤ 1/4

Symmetry operations

(1)  1
      (1 | 0, 0, 0)
(2)  2   0, 0, z
      (2z | 0, 0, 0)
(3)  4+ (1/2)   0, 0, z
      (4z | 0, 0, 1/2)
(4)  4- (1/2)   0, 0, z
      (4z-1 | 0, 0, 1/2)
(5)  2   0, y, 0
      (2y | 0, 0, 0)
(6)  2   x, 0, 0
      (2x | 0, 0, 0)
(7)  2   xx1/4
      (2xy | 0, 0, 1/2)
(8)  2   x-x1/4
      (2-xy | 0, 0, 1/2)

Generators selected (1); t(0, 0, 1); (2); (3); (5)

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions

 General:
8 h 1
(1) xyz(2) -x-yz(3) -yxz + 1/2(4) y-xz + 1/2
(5) -xy-z(6) x-y-z(7) yx-z + 1/2(8) -y-x-z + 1/2
l: l = 2n
  Special: no extra conditions
4 g  . . 2 
xx3/4-x-x3/4-xx1/4x-x1/4
4 f  . . 2 
xx1/4-x-x1/4-xx3/4x-x3/4
4 e  . 2 . 
x, 0, 1/2-x, 0, 1/20, x, 00, -x, 0
4 d  . 2 . 
x, 0, 0-x, 0, 00, x1/20, -x1/2
4 c  2 . . 
0, 0, z0, 0, z + 1/20, 0, -z0, 0, -z + 1/2
2 b  2 . 22 
0, 0, 1/40, 0, 3/4
2 a  2 22 . 
0, 0, 00, 0, 1/2

Symmetry of special projections

Along [001]   4mm

Origin at 0, 0, z
Along [100]   [script p]2mm
a' = c   
Origin at x, 0, 0
Along [110]   [script p]2mm
a' = c   
Origin at xx1/4

Maximal non-isotypic non-enantiomorphic subgroups


I[2] [script p]4211 ([script p]42, 25)1; 2; 3; 4
 [2] [script p]221 ([script p]222, 13)1; 2; 5; 6
 [2] [script p]212 ([script p]222, 13)1; 2; 7; 8
IIa none
IIb[2] [script p]4322 (c' = 2c) (33); [2] [script p]4122 (c' = 2c) (31)

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index


IIc[3] [script p]4222 (c' = 3c) (32)

Minimal non-isotypic non-enantiomorphic supergroups


I[2] [script p]42/mmc (41)
II[2] [script p]422 (c' = 1/2c) (30)








































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