[script p]-42m -42m Tetragonal
No. 37 [script p]-42m Patterson symmetry [script p]4/mmm
FIRST SETTING

symmetry group diagram

Origin at -42m

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

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, y, 0
      (2y | 0, 0, 0)
(6)  2   x, 0, 0
      (2x | 0, 0, 0)
(7)  m   x-xz
      (mxy | 0, 0, 0)
(8)  m   xxz
      (m-xy | 0, 0, 0)

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions

 General:
8 g 1
(1) xyz(2) -x-yz(3) y-x-z(4) -yx-z
(5) -xy-z(6) x-y-z(7) -y-xz(8) yxz
no conditions
  Special: no extra conditions
4 f  . . m 
xxz-x-xzx-x-z-xx-z
4 e  . 2 . 
x, 0, 1/2-x, 0, 1/20, -x1/20, x1/2
4 d  . 2 . 
x, 0, 0-x, 0, 00, -x, 00, x, 0
2 c  2 . mm 
0, 0, z0, 0, -z
1 b  -4 2 m 
0, 0, 1/2
1 a  -4 2 m 
0, 0, 0

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]11m
a' = c   
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]21m ([script p]mm2, 15)1; 2; 7; 8
 [2] [script p]221 ([script p]222, 13)1; 2; 5; 6
IIa none
IIb[2] [script p]-42c (c' = 2c) (38)

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index


IIc[2] [script p]-42m (c' = 2c) (37)

Minimal non-isotypic non-enantiomorphic supergroups


I[2] [script p]4/mmm (39); [2] [script p]42/mmc (41)
IInone
[script p]-4m2 -4m2 Tetragonal
No. 37 [script p]-4m2 Patterson symmetry [script p]4/mmm
SECOND SETTING

symmetry group diagram

Origin at -4m2

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

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)  m   x, 0, z
      (my | 0, 0, 0)
(6)  m   0, yz
      (mx | 0, 0, 0)
(7)  2   xx, 0
      (2xy | 0, 0, 0)
(8)  2   x-x, 0
      (2-xy | 0, 0, 0)

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions

 General:
8 g 1
(1) xyz(2) -x-yz(3) y-x-z(4) -yx-z
(5) x-yz(6) -xyz(7) yx-z(8) -y-x-z
no conditions
  Special: no extra conditions
4 f  . m . 
x, 0, z-x, 0, z0, -x-z0, x-z
4 e  . . 2 
xx1/2-x-x1/2x-x1/2-xx1/2
4 d  . . 2 
xx, 0-x-x, 0x-x, 0-xx, 0
2 c  2 mm . 
0, 0, z0, 0, -z
1 b  -4 m 2 
0, 0, 1/2
1 a  -4 m 2 
0, 0, 0

Symmetry of special projections

Along [001]   4mm

Origin at 0, 0, z
Along [100]   [script p]11m
a' = c   
Origin at x, 0, 0
Along [110]   [script p]2mm
a' = c   
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]2m1 ([script p]mm2, 15)1; 2; 5; 6
 [2] [script p]212 ([script p]222, 13)1; 2; 7; 8
IIa none
IIb[2] [script p]-4c2 (c' = 2c) ([script p]-42c, 38)

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index


IIc[2] [script p]-4m2 (c' = 2c) ([script p]-42m, 37)

Minimal non-isotypic non-enantiomorphic supergroups


I[2] [script p]4/mmm (39); [2] [script p]42/mmc (41)
IInone








































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