[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   (2)  2   0, 0, z(3)  4+(1/2)   0, 0, z(4)  4-(1/2)   0, 0, z
(5)  c   x, 0, z(6)  c   0, y, z(7)  m   x, -x, z(8)  m   x, x, z

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry		 Coordinates Reflection conditions
 General:
8 c 1
(1) x, y, z(2) -x, -y, z(3) -y, x, z + 1/2(4) y, -x, z + 1/2
(5) x, -y, z + 1/2(6) -x, y, z + 1/2(7) -y, -x, z(8) y, x, z
l: l = 2n
  Special: no extra conditions
4 b  . . m 
x, x, z-x, -x, z-x, x, z + 1/2x, -x, z + 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 x, x, 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   (2)  2   0, 0, z(3)  4+(1/2)   0, 0, z(4)  4-(1/2)   0, 0, z
(5)  m   x, 0, z(6)  m   0, y, z(7)  c   x, -x, z(8)  c   x, x, z

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry		 Coordinates Reflection conditions
 General:
8 c 1
(1) x, y, z(2) -x, -y, z(3) -y, x, z + 1/2(4) y, -x, z + 1/2
(5) x, -y, z(6) -x, y, z(7) -y, -x, z + 1/2(8) y, x, z + 1/2
l: l = 2n
  Special: no extra conditions
4 b  . m . 
x, 0, z-x, 0, z0, x, z + 1/20, -x, z + 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 x, x, 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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