Origin at -1 on glide plane a
| Asymmetric unit | 0 ≤ x ≤ 1/2; 0 ≤ y ≤ 1/2; 0 ≤ z ≤ 1/2 |
For (0, 0, 0)+ set
| (1) 1 | (2) 2 1/4, 0, z | (3) -1 0, 0, 0 | (4) a x, y, 0 |
For (0, 1/2, 1/2)+ set
| (1) t(0, 1/2, 1/2) | (2) 2(0, 0, 1/2) 1/4, 1/4, z | (3) -1 0, 1/4, 1/4 | (4) n(1/2, 1/2, 0) x, y, 1/4 |
Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); t(0, 1/2, 1/2); (2); (3)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates | Reflection conditions |
| | (0, 0, 0)+ (0, 1/2, 1/2)+ | General:
|
| | (1) x, y, z | (2) -x + 1/2, -y, z | (3) -x, -y, -z | (4) x + 1/2, y, -z |
| hkl : k + l = 2n
hk0 : h, k = 2n
0kl : k + l = 2n
h0l : l = 2n
00l : l = 2n
h00 : h = 2n
0k0 : k = 2n
|
| | | Special: as above, plus
|
| | no extra conditions |
| | 1/2, 1/4, 1/4 | 0, 3/4, 1/4 |
| hkl : h + k = 2n
|
| | 0, 1/4, 1/4 | 1/2, 3/4, 1/4 |
| hkl : h + k = 2n
|
| | hkl : h = 2n
|
| | hkl : h = 2n
|
Symmetry of special projections
Along [001] p2
a' = 1/2a b' = 1/2b
Origin at 0, 0, z | Along [100] c2mm
a' = bp b' = c
Origin at x, 0, 0 | Along [010] p2gm
a' = 1/2c b' = ap
Origin at 0, y, 0 |
Maximal non-isomorphic subgroups
| I | | [2] A11a (Cc, 9) | (1; 4)+ |
| | | [2] A112 (C2, 5) | (1; 2)+ |
| | | [2] A-1 (P-1, 2) | (1; 3)+ |
| IIa | | [2] P1121/n (P21/c, 14) | 1; 3; (2; 4) + (0, 1/2, 1/2) |
| | | [2] P1121/a (P21/c, 14) | 1; 4; (2; 3) + (0, 1/2, 1/2) |
| | | [2] P112/a (P2/c, 13) | 1; 2; 3; 4 |
| | | [2] P112/n (P2/c, 13) | 1; 2; (3; 4) + (0, 1/2, 1/2) |
Maximal isomorphic subgroups of lowest index
| IIc | [3] A112/a (c' = 3c) (C2/c, 15); [3] A112/a (a' = 3a) (C2/c, 15); [3] A112/a (b' = 3b or a' = a - b, b' = 3b or a' = a + b, b' = 3b) (C2/c, 15) |
Minimal non-isomorphic supergroups
| I | [2] Cmcm (63); [2] Cmce (64); [2] Cccm (66); [2] Ccce (68); [2] Fddd (70); [2] Ibam (72); [2] Ibca (73); [2] Imma (74); [2] I41/a (88); [3] P-31c (163); [3] P-3c1 (165); [3] R-3c (167) |
| II | [2] F112/m (C2/m, 12); [2] A112/m (a' = 1/2a) (C2/m, 12); [2] P112/a (b' = 1/2b, c' = 1/2c) (P2/c, 13) |
UNIQUE AXIS c, DIFFERENT CELL CHOICES
A112/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 ≤ 1/2 |
Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); t(0, 1/2, 1/2); (2); (3)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates | Reflection conditions |
| | (0, 0, 0)+ (0, 1/2, 1/2)+ | General:
|
| | (1) x, y, z | (2) -x + 1/2, -y, z | (3) -x, -y, -z | (4) x + 1/2, y, -z |
| hkl : k + l = 2n
hk0 : h, k = 2n
0kl : k + l = 2n
h0l : l = 2n
00l : l = 2n
h00 : h = 2n
0k0 : k = 2n
|
| | | Special: as above, plus
|
| | no extra conditions |
| | 1/2, 1/4, 1/4 | 0, 3/4, 1/4 |
| hkl : h + k = 2n |
| | 0, 1/4, 1/4 | 1/2, 3/4, 1/4 |
|
| | hkl : h = 2n |
| |
B112/n
UNIQUE AXIS c, CELL CHOICE 2
Origin at -1 on glide plane n
| Asymmetric unit | 0 ≤ x ≤ 1/4; 0 ≤ y ≤ 1/2; 0 ≤ z ≤ 1 |
Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); t(1/2, 0, 1/2); (2); (3)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates | Reflection conditions |
| | (0, 0, 0)+ (1/2, 0, 1/2)+ | 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 |
| hkl : h + l = 2n
hk0 : h, k = 2n
0kl : l = 2n
h0l : h + l = 2n
00l : l = 2n
h00 : h = 2n
0k0 : k = 2n
|
| | | Special: as above, plus
|
| | no extra conditions |
| | 3/4, 1/2, 1/4 | 3/4, 0, 1/4 |
| hkl : k = 2n |
| | 1/4, 0, 1/4 | 1/4, 1/2, 1/4 |
|
| | hkl : h + k = 2n |
| |
I112/b
UNIQUE AXIS c, CELL CHOICE 3
Origin at -1 on glide plane b
| Asymmetric unit | 0 ≤ x ≤ 1/4; 0 ≤ y ≤ 1; 0 ≤ z ≤ 1/2 |
Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); t(1/2, 1/2, 1/2); (2); (3)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates | Reflection conditions |
| | (0, 0, 0)+ (1/2, 1/2, 1/2)+ | General:
|
| | (1) x, y, z | (2) -x, -y + 1/2, z | (3) -x, -y, -z | (4) x, y + 1/2, -z |
| hkl : h + k + l = 2n
hk0 : h, k = 2n
0kl : k + l = 2n
h0l : h + l = 2n
00l : l = 2n
h00 : h = 2n
0k0 : k = 2n
|
| | | Special: as above, plus
|
| | no extra conditions |
| | 3/4, 1/4, 1/4 | 1/4, 1/4, 1/4 |
| hkl : h = 2n |
| | 3/4, 3/4, 1/4 | 1/4, 3/4, 1/4 |
|
| | hkl : k = 2n |
| |
