p112/a 2/m Monoclinic/Oblique No. 7 p112/a Patterson symmetry p112/m CELL CHOICE 1

Origin at -1 on glide plane a

 Asymmetric unit 0 ≤ x ≤ 1/2; 0 ≤ y ≤ 1/2; 0 ≤ z

Symmetry operations

 (1)  1       (1 | 0, 0, 0) (2)  2   1/4, 0, z       (2z | 1/2, 0, 0) (3)  -1   0, 0, 0       (-1 | 0, 0, 0) (4)  a   x, y, 0       (mz | 1/2, 0, 0)

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions

General:
 4 e 1
 (1) x, y, z (2) -x + 1/2, -y, z (3) -x, -y, -z (4) x + 1/2, y, -z
hk: h = 2n
h0: h = 2n
Special: no extra conditions
 2 d 2
 1/4, 1/2, z 3/4, 1/2, -z
 2 c 2
 1/4, 0, z 3/4, 0, -z
 2 b -1
 0, 1/2, 0 1/2, 1/2, 0
 2 a -1
 0, 0, 0 1/2, 0, 0

Symmetry of special projections

 Along [001]   p2 a' = 1/2a   b' = b    Origin at 0, 0, z Along [100]   2mm a' = bp    Origin at x, 0, 0 Along [010]   2mg a' = ap    Origin at 0, y, 0

Maximal non-isotypic subgroups

 I [2] p11a (5) 1; 4 [2] p112 (3) 1; 2 [2] p-1 (2) 1; 3
 IIa none
 IIb none

Maximal isotypic subgroups of lowest index

 IIc [2] p112/a (b' = 2b or a' = a + 2b, b' = 2b) (7)

Minimal non-isotypic supergroups

 I [2] pmaa (38); [2] pban (39); [2] pmma (41); [2] pman (42); [2] pbaa (43); [2] pbma (45); [2] pmmn (46); [2] cmme (48); [2] p4/n (52)
 II [2] p112/m (a' = 1/2a) (6)

DIFFERENT CELL CHOICES

p112/a

CELL CHOICE 1

Origin at -1 on glide plane a

 Asymmetric unit 0 ≤ x ≤ 1/2; 0 ≤ y ≤ 1/2; 0 ≤ z

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions

General:
 4 e 1
 (1) x, y, z (2) -x + 1/2, -y, z (3) -x, -y, -z (4) x + 1/2, y, -z
hk: h = 2n
h0: h = 2n
Special: no extra conditions
 2 d 2
 1/4, 1/2, z 3/4, 1/2, -z
 2 c 2
 1/4, 0, z 3/4, 0, -z
 2 b -1
 0, 1/2, 0 1/2, 1/2, 0
 2 a -1
 0, 0, 0 1/2, 0, 0

p112/n

CELL CHOICE 2

Origin at -1 on glide plane n

 Asymmetric unit 0 ≤ x ≤ 1/4; 0 ≤ y ≤ 1; 0 ≤ z

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions

General:
 4 e 1
 (1) x, y, z (2) -x + 1/2, -y + 1/2, z (3) -x, -y, -z (4) x + 1/2, y + 1/2, -z
hk: h + k = 2n
h0: h = 2n
0k: k = 2n
Special: no extra conditions
 2 d 2
 1/4, 3/4, z 3/4, 1/4, -z
 2 c 2
 3/4, 3/4, z 1/4, 1/4, -z
 2 b -1
 1/2, 0, 0 0, 1/2, 0
 2 a -1
 0, 0, 0 1/2, 1/2, 0

p112/b

CELL CHOICE 3

Origin at -1 on glide plane b

 Asymmetric unit 0 ≤ x ≤ 1/2; 0 ≤ y ≤ 1/2; 0 ≤ z

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions

General:
 4 e 1
 (1) x, y, z (2) -x, -y + 1/2, z (3) -x, -y, -z (4) x, y + 1/2, -z
hk: k = 2n
0k: k = 2n
Special: no extra conditions
 2 d 2
 1/2, 3/4, z 1/2, 1/4, -z
 2 c 2
 0, 1/4, z 0, 3/4, -z
 2 b -1
 1/2, 1/2, 0 1/2, 0, 0
 2 a -1
 0, 0, 0 0, 1/2, 0