Origin at -1
| Asymmetric unit | 0 ≤ x ≤ 1; 0 ≤ y ≤ 1/4; 0 ≤ z ≤ 1 |
| (1) 1 | (2) 2(0, 1/2, 0) 0, y, 1/4 | (3) -1 0, 0, 0 | (4) c x, 1/4, z |
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 + 1/2 | (3) -x, -y, -z | (4) x, -y + 1/2, z + 1/2 |
| h0l : l = 2n
0k0 : k = 2n
00l : l = 2n
|
| | | Special: as above, plus
|
| | hkl : k + l = 2n
|
| | hkl : k + l = 2n
|
| | hkl : k + l = 2n
|
| | hkl : k + l = 2n
|
Symmetry of special projections
Along [001] p2gm
a' = ap b' = b
Origin at 0, 0, z | Along [100] p2gg
a' = b b' = cp
Origin at x, 0, 0 | Along [010] p2
a' = 1/2c b' = a
Origin at 0, y, 0 |
Maximal non-isomorphic subgroups
| I | | [2] P1c1 (Pc, 7) | 1; 4 |
| | | [2] P1211 (P21, 4) | 1; 2 |
| | | [2] P-1 (2) | 1; 3 |
Maximal isomorphic subgroups of lowest index
| IIc | [2] P121/c1 (a' = 2a or a' = 2a, c' = 2a + c) (P21/c, 14); [3] P121/c1 (b' = 3b) (P21/c, 14) |
Minimal non-isomorphic supergroups
| I | [2] Pnna (52); [2] Pmna (53); [2] Pcca (54); [2] Pbam (55); [2] Pccn (56); [2] Pbcm (57); [2] Pnnm (58); [2] Pbcn (60); [2] Pbca (61); [2] Pnma (62); [2] Cmce (64) |
| II | [2] A12/m1 (C2/m, 12); [2] C12/c1 (C2/c, 15); [2] I12/c1 (C2/c, 15); [2] P121/m1 (c' = 1/2c) (P21/m, 11); [2] P12/c1 (b' = 1/2b) (P2/c, 13) |
UNIQUE AXIS b, DIFFERENT CELL CHOICES
P121/c1
UNIQUE AXIS b, CELL CHOICE 1
Origin at -1
| Asymmetric unit | 0 ≤ x ≤ 1; 0 ≤ y ≤ 1/4; 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 + 1/2 | (3) -x, -y, -z | (4) x, -y + 1/2, z + 1/2 |
| h0l : l = 2n
0k0 : k = 2n
00l : l = 2n
|
| | | Special: as above, plus
|
| | hkl : k + l = 2n
|
| | hkl : k + l = 2n
|
| | hkl : k + l = 2n
|
| | hkl : k + l = 2n
|
P121/n1
UNIQUE AXIS b, CELL CHOICE 2
Origin at -1
| Asymmetric unit | 0 ≤ x ≤ 1; 0 ≤ y ≤ 1/4; 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 + 1/2 | (3) -x, -y, -z | (4) x + 1/2, -y + 1/2, z + 1/2 |
| h0l : h + l = 2n
0k0 : k = 2n
h00 : h = 2n
00l : l = 2n
|
| | | Special: as above, plus
|
| | hkl : h + k + l = 2n
|
| | hkl : h + k + l = 2n
|
| | hkl : h + k + l = 2n
|
| | hkl : h + k + l = 2n
|
P121/a1
UNIQUE AXIS b, CELL CHOICE 3
Origin at -1
| Asymmetric unit | 0 ≤ x ≤ 1; 0 ≤ y ≤ 1/4; 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 |
| h0l : h = 2n
0k0 : k = 2n
h00 : h = 2n
|
| | | Special: as above, plus
|
| | hkl : h + k = 2n
|
| | hkl : h + k = 2n
|
| | hkl : h + k = 2n
|
| | hkl : h + k = 2n
|
Origin at -1
| Asymmetric unit | 0 ≤ x ≤ 1; 0 ≤ y ≤ 1; 0 ≤ z ≤ 1/4 |
| (1) 1 | (2) 2(0, 0, 1/2) 1/4, 0, z | (3) -1 0, 0, 0 | (4) a x, y, 1/4 |
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 + 1/2 | (3) -x, -y, -z | (4) x + 1/2, y, -z + 1/2 |
| hk0 : h = 2n
00l : l = 2n
h00 : h = 2n
|
| | | Special: as above, plus
|
| | hkl : h + l = 2n
|
| | hkl : h + l = 2n
|
| | hkl : h + l = 2n
|
| | hkl : h + l = 2n
|
Symmetry of special projections
Along [001] p2
a' = 1/2a b' = b
Origin at 0, 0, z | Along [100] p2gm
a' = bp b' = c
Origin at x, 0, 0 | Along [010] p2gg
a' = c b' = ap
Origin at 0, y, 0 |
Maximal non-isomorphic subgroups
| I | | [2] P11a (Pc, 7) | 1; 4 |
| | | [2] P1121 (P21, 4) | 1; 2 |
| | | [2] P-1 (2) | 1; 3 |
Maximal isomorphic subgroups of lowest index
| IIc | [2] P1121/a (b' = 2b or a' = a + 2b, b' = 2b) (P21/c, 14); [3] P1121/a (c' = 3c) (P21/c, 14) |
Minimal non-isomorphic supergroups
| I | [2] Pnna (52); [2] Pmna (53); [2] Pcca (54); [2] Pbam (55); [2] Pccn (56); [2] Pbcm (57); [2] Pnnm (58); [2] Pbcn (60); [2] Pbca (61); [2] Pnma (62); [2] Cmce (64) |
| II | [2] A112/a (C2/c, 15); [2] B112/m (C2/m, 12); [2] I112/a (C2/c, 15); [2] P1121/m (a' = 1/2a) (P21/m, 11); [2] P112/a (c' = 1/2c) (P2/c, 13) |
UNIQUE AXIS c, DIFFERENT CELL CHOICES
P1121/a
UNIQUE AXIS c, CELL CHOICE 1
Origin at -1
| 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)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates | Reflection conditions |
| | | General:
|
| | (1) x, y, z | (2) -x + 1/2, -y, z + 1/2 | (3) -x, -y, -z | (4) x + 1/2, y, -z + 1/2 |
| hk0 : h = 2n
00l : l = 2n
h00 : h = 2n
|
| | | Special: as above, plus
|
| | hkl : h + l = 2n
|
| | hkl : h + l = 2n
|
| | hkl : h + l = 2n
|
| | hkl : h + l = 2n
|
P1121/n
UNIQUE AXIS c, CELL CHOICE 2
Origin at -1
| 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)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates | Reflection conditions |
| | | General:
|
| | (1) x, y, z | (2) -x + 1/2, -y + 1/2, z + 1/2 | (3) -x, -y, -z | (4) x + 1/2, y + 1/2, -z + 1/2 |
| hk0 : h + k = 2n
00l : l = 2n
h00 : h = 2n
0k0 : k = 2n
|
| | | Special: as above, plus
|
| | hkl : h + k + l = 2n
|
| | hkl : h + k + l = 2n
|
| | hkl : h + k + l = 2n
|
| | hkl : h + k + l = 2n
|
P1121/b
UNIQUE AXIS c, CELL CHOICE 3
Origin at -1
| 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)
Multiplicity, Wyckoff letter,
Site symmetry | Coordinates | Reflection conditions |
| | | General:
|
| | (1) x, y, z | (2) -x, -y + 1/2, z + 1/2 | (3) -x, -y, -z | (4) x, y + 1/2, -z + 1/2 |
| hk0 : k = 2n
00l : l = 2n
0k0 : k = 2n
|
| | | Special: as above, plus
|
| | hkl : k + l = 2n
|
| | hkl : k + l = 2n
|
| | hkl : k + l = 2n
|
| | hkl : k + l = 2n
|
