[script p]-42c -42m Tetragonal
No. 38 [script p]-42c Patterson symmetry [script p]4/mmm
FIRST SETTING

symmetry group diagram

Origin at -41c

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

Symmetry operations

(1)  1
      (1 | 0, 0, 0)
(2)  2   0, 0, z
      (2z | 0, 0, 0)
(3)  -4+   0, 0, z; 0, 0, 0
      (-4z | 0, 0, 0)
(4)  -4-   0, 0, z; 0, 0, 0
      (-4z-1 | 0, 0, 0)
(5)  2   0, y1/4
      (2y | 0, 0, 1/2)
(6)  2   x, 0, 1/4
      (2x | 0, 0, 1/2)
(7)  c   x-xz
      (mxy | 0, 0, 1/2)
(8)  c   xxz
      (m-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 f 1
(1) xyz(2) -x-yz(3) y-x-z(4) -yx-z
(5) -xy-z + 1/2(6) x-y-z + 1/2(7) -y-xz + 1/2(8) yxz + 1/2
l: l = 2n
  Special: no extra conditions
4 e  2 . . 
0, 0, z0, 0, -z0, 0, -z + 1/20, 0, z + 1/2
4 d  . 2 . 
0, y1/40, -y1/4y, 0, 3/4-y, 0, 3/4
4 c  . 2 . 
x, 0, 1/4-x, 0, 1/40, -x3/40, x3/4
2 b  -4 . . 
0, 0, 00, 0, 1/2
2 a  2 22 . 
0, 0, 1/40, 0, 3/4

Symmetry of special projections

Along [001]   4mm

Origin at 0, 0, z
Along [100]   [script p]2mm
a' = c   
Origin at x, 0, 1/4
Along [110]   [script p]11m
a' = 1/2c   
Origin at xx, 0

Maximal non-isotypic non-enantiomorphic subgroups


I[2] [script p]-411 ([script p]-4, 27)1; 2; 3; 4
 [2] [script p]21c ([script p]cc2, 16)1; 2; 7; 8
 [2] [script p]221 ([script p]222, 13)1; 2; 5; 6
IIa none
IIbnone

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index


IIc[3] [script p]-42c (c' = 3c) (38)

Minimal non-isotypic non-enantiomorphic supergroups


I[2] [script p]4/mcc (40); [2] [script p]42/mmc (41)
II[2] [script p]-42m (c' = 1/2c) (37)
[script p]-4c2 -4m2 Tetragonal
No. 38 [script p]-4c2 Patterson symmetry [script p]4/mmm
SECOND SETTING

symmetry group diagram

Origin at -4c1

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

Symmetry of special projections

Along [001]   4mm

Origin at 0, 0, z
Along [100]   [script p]11m
a' = 1/2c   
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]-411 ([script p]-4, 27)1; 2; 3; 4
 [2] [script p]2c1 ([script p]cc2, 16)1; 2; 5; 6
 [2] [script p]212 ([script p]222, 13)1; 2; 7; 8
IIa none
IIbnone

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index


IIc[3] [script p]-4c2 (c' = 3c) ([script p]-42c, 38)

Minimal non-isotypic non-enantiomorphic supergroups


I[2] [script p]4/mcc (40); [2] [script p]42/mmc (41)
II[2] [script p]-42m (c' = 1/2c) (37)








































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