P2/c C2h4 2/m Monoclinic No. 13 P12/c1 Patterson symmetry P12/m1 UNIQUE AXIS b, CELL CHOICE 1

Origin at -1 on glide plane c

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

Symmetry operations

 (1)  1 (2)  2   0, y, 1/4 (3)  -1   0, 0, 0 (4)  c   x, 0, z

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
General:
 4 g 1
 (1) x, y, z (2) -x, y, -z + 1/2 (3) -x, -y, -z (4) x, -y, z + 1/2
h0l : l = 2n
00l : l = 2n
Special: as above, plus
 2 f 2
 1/2, y, 1/4 1/2, -y, 3/4
no extra conditions
 2 e 2
 0, y, 1/4 0, -y, 3/4
no extra conditions
 2 d -1
 1/2, 0, 0 1/2, 0, 1/2
hkl : l = 2n
 2 c -1
 0, 1/2, 0 0, 1/2, 1/2
hkl : l = 2n
 2 b -1
 1/2, 1/2, 0 1/2, 1/2, 1/2
hkl : l = 2n
 2 a -1
 0, 0, 0 0, 0, 1/2
hkl : l = 2n

Symmetry of special projections

 Along [001]   p2mma' = ap   b' = b   Origin at 0, 0, z Along [100]   p2gma' = b   b' = cp   Origin at x, 0, 0 Along [010]   p2a' = 1/2c   b' = a   Origin at 0, y, 0

Maximal non-isomorphic subgroups

 I [2] P1c1 (Pc, 7) 1; 4 [2] P121 (P2, 3) 1; 2 [2] P-1 (2) 1; 3
 IIa none
 IIb [2] P121/c1 (b' = 2b) (P21/c, 14); [2] C12/c1 (a' = 2a, b' = 2b) (C2/c, 15)

Maximal isomorphic subgroups of lowest index

 IIc [2] P12/c1 (b' = 2b) (P2/c, 13); [2] P12/c1 (a' = 2a or a' = 2a, c' = 2a + c) (P2/c, 13)

Minimal non-isomorphic supergroups

 I [2] Pnnn (48); [2] Pccm (49); [2] Pban (50); [2] Pmma (51); [2] Pnna (52); [2] Pmna (53); [2] Pcca (54); [2] Pccn (56); [2] Pbcm (57); [2] Pmmn (59); [2] Pbcn (60); [2] Cmme (67); [2] Ccce (68); [2] P4/n (85); [2] P42/n (86)
 II [2] A12/m1 (C2/m, 12); [2] C12/c1 (C2/c, 15); [2] I12/c1 (C2/c, 15); [2] P12/m1 (c' = 1/2c) (P2/m, 10)

UNIQUE AXIS b, DIFFERENT CELL CHOICES

P12/c1

UNIQUE AXIS b, CELL CHOICE 1

Origin at -1 on glide plane c

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

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
General:
 4 g 1
 (1) x, y, z (2) -x, y, -z + 1/2 (3) -x, -y, -z (4) x, -y, z + 1/2
h0l : l = 2n
00l : l = 2n
Special: as above, plus
 2 f 2
 1/2, y, 1/4 1/2, -y, 3/4
no extra conditions
 2 e 2
 0, y, 1/4 0, -y, 3/4
no extra conditions
 2 d -1
 1/2, 0, 0 1/2, 0, 1/2
hkl : l = 2n
 2 c -1
 0, 1/2, 0 0, 1/2, 1/2
 2 b -1
 1/2, 1/2, 0 1/2, 1/2, 1/2
hkl : l = 2n
 2 a -1
 0, 0, 0 0, 0, 1/2

P12/n1

UNIQUE AXIS b, CELL CHOICE 2

Origin at -1 on glide plane n

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

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
General:
 4 g 1
 (1) x, y, z (2) -x + 1/2, y, -z + 1/2 (3) -x, -y, -z (4) x + 1/2, -y, z + 1/2
h0l : h + l = 2n
h00 : h = 2n
00l : l = 2n
Special: as above, plus
 2 f 2
 3/4, y, 1/4 1/4, -y, 3/4
no extra conditions
 2 e 2
 3/4, y, 3/4 1/4, -y, 1/4
no extra conditions
 2 d -1
 0, 0, 1/2 1/2, 0, 0
hkl : h + l = 2n
 2 c -1
 0, 1/2, 0 1/2, 1/2, 1/2
 2 b -1
 0, 1/2, 1/2 1/2, 1/2, 0
hkl : h + l = 2n
 2 a -1
 0, 0, 0 1/2, 0, 1/2

P12/a1

UNIQUE AXIS b, CELL CHOICE 3

Origin at -1 on glide plane a

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

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
General:
 4 g 1
 (1) x, y, z (2) -x + 1/2, y, -z (3) -x, -y, -z (4) x + 1/2, -y, z
h0l : h = 2n
h00 : h = 2n
Special: as above, plus
 2 f 2
 3/4, y, 1/2 1/4, -y, 1/2
no extra conditions
 2 e 2
 1/4, y, 0 3/4, -y, 0
no extra conditions
 2 d -1
 1/2, 0, 1/2 0, 0, 1/2
hkl : h = 2n
 2 c -1
 0, 1/2, 0 1/2, 1/2, 0
 2 b -1
 1/2, 1/2, 1/2 0, 1/2, 1/2
hkl : h = 2n
 2 a -1
 0, 0, 0 1/2, 0, 0

 P2/c C2h4 2/m Monoclinic No. 13 P112/a Patterson symmetry P112/m UNIQUE AXIS c, CELL CHOICE 1

Origin at -1 on glide plane a

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

Symmetry operations

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

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
General:
 4 g 1
 (1) x, y, z (2) -x + 1/2, -y, z (3) -x, -y, -z (4) x + 1/2, y, -z
hk0 : h = 2n
h00 : h = 2n
Special: as above, plus
 2 f 2
 1/4, 1/2, z 3/4, 1/2, -z
no extra conditions
 2 e 2
 1/4, 0, z 3/4, 0, -z
no extra conditions
 2 d -1
 0, 1/2, 0 1/2, 1/2, 0
hkl : h = 2n
 2 c -1
 0, 0, 1/2 1/2, 0, 1/2
hkl : h = 2n
 2 b -1
 0, 1/2, 1/2 1/2, 1/2, 1/2
hkl : h = 2n
 2 a -1
 0, 0, 0 1/2, 0, 0
hkl : h = 2n

Symmetry of special projections

 Along [001]   p2a' = 1/2a   b' = b   Origin at 0, 0, z Along [100]   p2mma' = bp   b' = c   Origin at x, 0, 0 Along [010]   p2gma' = c   b' = ap   Origin at 0, y, 0

Maximal non-isomorphic subgroups

 I [2] P11a (Pc, 7) 1; 4 [2] P112 (P2, 3) 1; 2 [2] P-1 (2) 1; 3
 IIa none
 IIb [2] P1121/a (c' = 2c) (P21/c, 14); [2] A112/a (b' = 2b, c' = 2c) (C2/c, 15)

Maximal isomorphic subgroups of lowest index

 IIc [2] P112/a (c' = 2c) (P2/c, 13); [2] P112/a (b' = 2b or a' = a + 2b, b' = 2b) (P2/c, 13)

Minimal non-isomorphic supergroups

 I [2] Pnnn (48); [2] Pccm (49); [2] Pban (50); [2] Pmma (51); [2] Pnna (52); [2] Pmna (53); [2] Pcca (54); [2] Pccn (56); [2] Pbcm (57); [2] Pmmn (59); [2] Pbcn (60); [2] Cmme (67); [2] Ccce (68); [2] P4/n (85); [2] P42/n (86)
 II [2] A112/a (C2/c, 15); [2] B112/m (C2/m, 12); [2] I112/a (C2/c, 15); [2] P112/m (a' = 1/2a) (P2/m, 10)

UNIQUE AXIS c, DIFFERENT CELL CHOICES

P112/a

UNIQUE AXIS c, CELL CHOICE 1

Origin at -1 on glide plane a

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

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
General:
 4 g 1
 (1) x, y, z (2) -x + 1/2, -y, z (3) -x, -y, -z (4) x + 1/2, y, -z
hk0 : h = 2n
h00 : h = 2n
Special: as above, plus
 2 f 2
 1/4, 1/2, z 3/4, 1/2, -z
no extra conditions
 2 e 2
 1/4, 0, z 3/4, 0, -z
no extra conditions
 2 d -1
 0, 1/2, 0 1/2, 1/2, 0
hkl : h = 2n
 2 c -1
 0, 0, 1/2 1/2, 0, 1/2
 2 b -1
 0, 1/2, 1/2 1/2, 1/2, 1/2
hkl : h = 2n
 2 a -1
 0, 0, 0 1/2, 0, 0

P112/n

UNIQUE AXIS c, CELL CHOICE 2

Origin at -1 on glide plane n

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

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
General:
 4 g 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
hk0 : h + k = 2n
h00 : h = 2n
0k0 : k = 2n
Special: as above, plus
 2 f 2
 1/4, 3/4, z 3/4, 1/4, -z
no extra conditions
 2 e 2
 3/4, 3/4, z 1/4, 1/4, -z
no extra conditions
 2 d -1
 1/2, 0, 0 0, 1/2, 0
hkl : h + k = 2n
 2 c -1
 0, 0, 1/2 1/2, 1/2, 1/2
 2 b -1
 1/2, 0, 1/2 0, 1/2, 1/2
hkl : h + k = 2n
 2 a -1
 0, 0, 0 1/2, 1/2, 0

P112/b

UNIQUE AXIS c, CELL CHOICE 3

Origin at -1 on glide plane b

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

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

Positions

Multiplicity, Wyckoff letter,
Site symmetry
Coordinates Reflection conditions
General:
 4 g 1
 (1) x, y, z (2) -x, -y + 1/2, z (3) -x, -y, -z (4) x, y + 1/2, -z
hk0 : k = 2n
0k0 : k = 2n
Special: as above, plus
 2 f 2
 1/2, 3/4, z 1/2, 1/4, -z
no extra conditions
 2 e 2
 0, 1/4, z 0, 3/4, -z
no extra conditions
 2 d -1
 1/2, 1/2, 0 1/2, 0, 0
hkl : k = 2n
 2 c -1
 0, 0, 1/2 0, 1/2, 1/2
 2 b -1
 1/2, 1/2, 1/2 1/2, 0, 1/2
hkl : k = 2n
 2 a -1
 0, 0, 0 0, 1/2, 0