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

symmetry group diagram

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   xy, 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) xyz (2) -x + 1/2-yz (3) -x-y-z (4) x + 1/2y-z
hk: h = 2n
h0: h = 2n
    Special: no extra conditions
2 d  2 
1/41/2z 3/41/2-z
2 c  2 
1/4, 0, z 3/4, 0, -z
2 b  -1 
0, 1/2, 0 1/21/2, 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]   [script p]2mm
a' = bp   
Origin at x, 0, 0
Along [010]   [script p]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 + 2bb' = 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

symmetry group diagram

p112/a

CELL CHOICE 1

symmetry group diagram

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) xyz (2) -x + 1/2-yz (3) -x-y-z (4) x + 1/2y-z
hk: h = 2n
h0: h = 2n
    Special: no extra conditions
2 d  2 
1/41/2z 3/41/2-z
2 c  2 
1/4, 0, z 3/4, 0, -z
2 b  -1 
0, 1/2, 0 1/21/2, 0
2 a  -1 
0, 0, 0 1/2, 0, 0

p112/n

CELL CHOICE 2

symmetry group diagram

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) xyz (2) -x + 1/2-y + 1/2z (3) -x-y-z (4) x + 1/2y + 1/2-z
hk: h + k = 2n
h0: h = 2n
0k: k = 2n
    Special: no extra conditions
2 d  2 
1/43/4z 3/41/4-z
2 c  2 
3/43/4z 1/41/4-z
2 b  -1 
1/2, 0, 0 0, 1/2, 0
2 a  -1 
0, 0, 0 1/21/2, 0

p112/b

CELL CHOICE 3

symmetry group diagram

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) xyz (2) -x-y + 1/2z (3) -x-y-z (4) xy + 1/2-z
hk: k = 2n
0k: k = 2n
    Special: no extra conditions
2 d  2 
1/23/4z 1/21/4-z
2 c  2 
0, 1/4z 0, 3/4-z
2 b  -1 
1/21/2, 0 1/2, 0, 0
2 a  -1 
0, 0, 0 0, 1/2, 0








































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