[script p]4mm 4mm Tetragonal
No. 34 [script p]4mm Patterson symmetry [script p]4/mmm

symmetry group diagram

Origin on 4mm

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
      (4z | 0, 0, 0)
(4)  4-   0, 0, z
      (4z-1 | 0, 0, 0)
(5)  m   x, 0, z
      (my | 0, 0, 0)
(6)  m   0, yz
      (mx | 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 d 1
(1) xyz(2) -x-yz(3) -yxz(4) y-xz
(5) x-yz(6) -xyz(7) -y-xz(8) yxz
no conditions
  Special: no extra conditions
4 c  . m . 
x, 0, z-x, 0, z0, xz0, -xz
4 b  . . m 
xxz-x-xz-xxzx-xz
1 a  4 m m 
0, 0, z

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]11m
a' = c   
Origin at xx, 0

Maximal non-isotypic non-enantiomorphic subgroups


I[2] [script p]411 ([script p]4, 23)1; 2; 3; 4
 [2] [script p]2m1 ([script p]mm2, 15)1; 2; 5; 6
 [2] [script p]21m ([script p]mm2, 15)1; 2; 7; 8
IIa none
IIb[2] [script p]4cc (c' = 2c) (36); [2] [script p]42mc (c' = 2c) ([script p]42cm, 35); [2] [script p]42cm (c' = 2c) (35)

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index


IIc[2] [script p]4mm (c' = 2c) (34)

Minimal non-isotypic non-enantiomorphic supergroups


I[2] [script p]4/mmm (39)
IInone








































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