[script p]42cm 4mm Tetragonal
No. 35 [script p]42cm Patterson symmetry [script p]4/mmm
FIRST SETTING

symmetry group diagram

Origin on 2mm on 42cm

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+ (1/2)   0, 0, z
      (4z | 0, 0, 1/2)
(4)  4- (1/2)   0, 0, z
      (4z-1 | 0, 0, 1/2)
(5)  c   x, 0, z
      (my | 0, 0, 1/2)
(6)  c   0, yz
      (mx | 0, 0, 1/2)
(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 c 1
(1) xyz(2) -x-yz(3) -yxz + 1/2(4) y-xz + 1/2
(5) x-yz + 1/2(6) -xyz + 1/2(7) -y-xz(8) yxz
l: l = 2n
  Special: no extra conditions
4 b  . . m 
xxz-x-xz-xxz + 1/2x-xz + 1/2
2 a  2 . mm 
0, 0, z0, 0, z + 1/2

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]11m
a' = c   
Origin at xx, 0

Maximal non-isotypic non-enantiomorphic subgroups


I[2] [script p]4211 ([script p]42, 25)1; 2; 3; 4
 [2] [script p]2c1 ([script p]cc2, 16)1; 2; 5; 6
 [2] [script p]21m ([script p]mm2, 15)1; 2; 7; 8
IIa none
IIbnone

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index


IIc[3] [script p]42cm (c' = 3c) (35)

Minimal non-isotypic non-enantiomorphic supergroups


I[2] [script p]42/mmc (41)
II[2] [script p]4mm (c' = 1/2c) (34)
[script p]42mc 4mm Tetragonal
No. 35 [script p]42mc Patterson symmetry [script p]4/mmm
SECOND SETTING

symmetry group diagram

Origin on 2mm on 42mc

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+ (1/2)   0, 0, z
      (4z | 0, 0, 1/2)
(4)  4- (1/2)   0, 0, z
      (4z-1 | 0, 0, 1/2)
(5)  m   x, 0, z
      (my | 0, 0, 0)
(6)  m   0, yz
      (mx | 0, 0, 0)
(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 c 1
(1) xyz(2) -x-yz(3) -yxz + 1/2(4) y-xz + 1/2
(5) x-yz(6) -xyz(7) -y-xz + 1/2(8) yxz + 1/2
l: l = 2n
  Special: no extra conditions
4 b  . m . 
x, 0, z-x, 0, z0, xz + 1/20, -xz + 1/2
2 a  2 mm . 
0, 0, z0, 0, z + 1/2

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' = 1/2c   
Origin at xx, 0

Maximal non-isotypic non-enantiomorphic subgroups


I[2] [script p]4211 ([script p]42, 25)1; 2; 3; 4
 [2] [script p]21c ([script p]cc2, 16)1; 2; 7; 8
 [2] [script p]2m1 ([script p]mm2, 15)1; 2; 5; 6
IIa none
IIbnone

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index


IIc[3] [script p]42mc (c' = 3c) ([script p]42cm, 35)

Minimal non-isotypic non-enantiomorphic supergroups


I[2] [script p]42/mmc (41)
II[2] [script p]4mm (c' = 1/2c) (34)








































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