42cm 4mm Tetragonal No. 35 42cm Patterson symmetry 4/mmm FIRST SETTING

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, y, z      (mx | 0, 0, 1/2) (7)  m   x, -x, z      (mxy | 0, 0, 0) (8)  m   x, x, z      (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) 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 + 1/2 x, -x, z + 1/2
 2 a 2 . mm
 0, 0, z 0, 0, z + 1/2

Symmetry of special projections

 Along [001]   4mmOrigin at 0, 0, z Along [100]   11ma' = 1/2c   Origin at x, 0, 0 Along [110]   11ma' = c   Origin at x, x, 0

Maximal non-isotypic non-enantiomorphic subgroups

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

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index

 IIc [3] 42cm (c' = 3c) (35)

Minimal non-isotypic non-enantiomorphic supergroups

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

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, y, z      (mx | 0, 0, 0) (7)  c   x, -x, z      (mxy | 0, 0, 1/2) (8)  c   x, x, z      (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) 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, z 0, x, z + 1/2 0, -x, z + 1/2
 2 a 2 mm .
 0, 0, z 0, 0, z + 1/2

Symmetry of special projections

 Along [001]   4mmOrigin at 0, 0, z Along [100]   11ma' = c   Origin at x, 0, 0 Along [110]   11ma' = 1/2c   Origin at x, x, 0

Maximal non-isotypic non-enantiomorphic subgroups

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

Maximal isotypic subgroups and enantiomorphic subgroups of lowest index

 IIc [3] 42mc (c' = 3c) (42cm, 35)

Minimal non-isotypic non-enantiomorphic supergroups

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