
Origin at -1 on glide plane c
Asymmetric unit | 0 ≤ x ≤ 1/2; 0 ≤ y ≤ 1/2; 0 ≤ z ≤ 1/2 |
For (0, 0, 0)+ set
(1) 1 | (2) 2 0, y, 1/4 | (3) -1 0, 0, 0 | (4) c x, 0, z |
For (1/2, 1/2, 0)+ set
(1) t(1/2, 1/2, 0) | (2) 2(0, 1/2, 0) 1/4, y, 1/4 | (3) -1 1/4, 1/4, 0 | (4) n(1/2, 0, 1/2) x, 1/4, z |
Generators selected (1); t(1, 0, 0); t(0, 1, 0); t(0, 0, 1); t(1/2, 1/2, 0); (2); (3)
Multiplicity, Wyckoff letter, Site symmetry | Coordinates | Reflection conditions |
| (0, 0, 0)+ (1/2, 1/2, 0)+ | General:
|
| (1) x, y, z | (2) -x, y, -z + 1/2 | (3) -x, -y, -z | (4) x, -y, z + 1/2 |
| hkl: h + k = 2n h0l: h, l = 2n 0kl: k = 2n hk0: h + k = 2n 0k0: k = 2n h00: h = 2n 00l: l = 2n
|
| | Special: as above, plus
|
| | no extra conditions |
| 1/4, 1/4, 1/2 | 3/4, 1/4, 0 |
| hkl: k + l = 2n
|
| 1/4, 1/4, 0 | 3/4, 1/4, 1/2 |
| hkl: k + l = 2n
|
| | hkl: l = 2n
|
| | hkl: l = 2n
|
Symmetry of special projections
Along [001] c2mm a' = ap b' = b Origin at 0, 0, z | Along [100] p2gm a' = 1/2b b' = cp Origin at x, 0, 0 | Along [010] p2 a' = 1/2c b' = 1/2a Origin at 0, y, 0 |
UNIQUE AXIS b, DIFFERENT CELL CHOICES

C12/c1
UNIQUE AXIS b, CELL CHOICE 1

Origin at -1 on glide plane c
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(1/2, 1/2, 0); (2); (3)
Multiplicity, Wyckoff letter, Site symmetry | Coordinates | Reflection conditions |
| (0, 0, 0)+ (1/2, 1/2, 0)+ | General:
|
| (1) x, y, z | (2) -x, y, -z + 1/2 | (3) -x, -y, -z | (4) x, -y, z + 1/2 |
| hkl: h + k = 2n h0l: h, l = 2n 0kl: k = 2n hk0: h + k = 2n 0k0: k = 2n h00: h = 2n 00l: l = 2n
|
| | Special: as above, plus
|
| | no extra conditions |
| 1/4, 1/4, 1/2 | 3/4, 1/4, 0 |
| hkl: k + l = 2n |
| 1/4, 1/4, 0 | 3/4, 1/4, 1/2 |
|
| | hkl: l = 2n |
| |
A12/n1
UNIQUE AXIS b, CELL CHOICE 2

Origin at -1 on glide plane n
Asymmetric unit | 0 ≤ x ≤ 1/2; 0 ≤ y ≤ 1; 0 ≤ z ≤ 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 + 1/2 | (3) -x, -y, -z | (4) x + 1/2, -y, z + 1/2 |
| hkl: k + l = 2n h0l: h, l = 2n 0kl: k + l = 2n hk0: k = 2n 0k0: k = 2n h00: h = 2n 00l: l = 2n
|
| | Special: as above, plus
|
| | no extra conditions |
| 1/2, 1/4, 3/4 | 0, 1/4, 3/4 |
| hkl: h = 2n |
| 0, 1/4, 1/4 | 1/2, 1/4, 1/4 |
|
| | hkl: h + k = 2n |
| |
I12/a1
UNIQUE AXIS b, CELL CHOICE 3

Origin at -1 on glide plane a
Asymmetric unit | 0 ≤ x ≤ 1; 0 ≤ y ≤ 1/2; 0 ≤ z ≤ 1/4 |
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 + 1/2, y, -z | (3) -x, -y, -z | (4) x + 1/2, -y, z |
| hkl: h + k + l = 2n h0l: h, l = 2n 0kl: k + l = 2n hk0: h + k = 2n 0k0: k = 2n h00: h = 2n 00l: l = 2n
|
| | Special: as above, plus
|
| | no extra conditions |
| 1/4, 1/4, 3/4 | 1/4, 1/4, 1/4 |
| hkl: l = 2n |
| 3/4, 1/4, 3/4 | 3/4, 1/4, 1/4 |
|
| | hkl: h = 2n |
| |

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 |
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 |
| |