Origin at -1 on glide plane a
Asymmetric unit | 0 ≤ x ≤ 1/2; 0 ≤ y ≤ 1/2; 0 ≤ z ≤ 1 |
(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)
Multiplicity, Wyckoff letter, Site symmetry | Coordinates | Reflection conditions |
| | General:
|
| (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
|
| | no extra conditions |
| | no extra conditions |
| | hkl : h = 2n
|
| | hkl : h = 2n
|
| 0, 1/2, 1/2 | 1/2, 1/2, 1/2 |
| hkl : h = 2n
|
| | hkl : h = 2n
|
Symmetry of special projections
Along [001] p2 a' = 1/2a b' = b Origin at 0, 0, z | Along [100] p2mm a' = bp b' = c Origin at x, 0, 0 | Along [010] p2gm a' = 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 |
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)
Multiplicity, Wyckoff letter, Site symmetry | Coordinates | Reflection conditions |
| | General:
|
| (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
|
| | no extra conditions |
| | no extra conditions |
| | hkl : h = 2n |
| |
| 0, 1/2, 1/2 | 1/2, 1/2, 1/2 |
| hkl : h = 2n |
| |
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)
Multiplicity, Wyckoff letter, Site symmetry | Coordinates | Reflection conditions |
| | General:
|
| (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
|
| | no extra conditions |
| | no extra conditions |
| | hkl : h + k = 2n |
| |
| | hkl : h + k = 2n |
| |
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)
Multiplicity, Wyckoff letter, Site symmetry | Coordinates | Reflection conditions |
| | General:
|
| (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
|
| | no extra conditions |
| | no extra conditions |
| | hkl : k = 2n |
| |
| 1/2, 1/2, 1/2 | 1/2, 0, 1/2 |
| hkl : k = 2n |
| |