Crystal Lab › The 230 space groups › Hexagonal
No. 181 P6₄22
Hexagonal space group · 12 symmetry operations per cell · 11 Wyckoff positions
Symmetry elements and Wyckoff positions (interactive)
No. 181 P6₄22
SettingLoading the group…
x = 0.10, y = 0.17, z = 0.08
- Number
- 181
- Hermann–Mauguin symbol
- P6₄22
- Hall symbol
P6₄ 2 (0 0 2)- Crystal system
- Hexagonal
- Operations per cell
- 12
- General position
- 12k (site symmetry 1)
Wyckoff positions (standard setting)
| Multiplicity | Letter | Site symmetry |
|---|---|---|
| 12 | k | 1 |
| 6 | j | ..2 |
| 6 | i | ..2 |
| 6 | h | .2. |
| 6 | g | .2. |
| 6 | f | 2.. |
| 6 | e | 2.. |
| 3 | d | 222 |
| 3 | c | 222 |
| 3 | b | 222 |
| 3 | a | 222 |
How to read it
- Each symmetry element drawn in the cell is worked out from the group’s operations: rotation and screw axes as lines (arrow = direction; dashed = screw), mirror and glide planes as sheets (dashed outline = glide), inversion centres as dots; rotoinversion axes are dotted. Colours: 2-fold red, 3-fold green, 4-fold blue, 6-fold purple.
- The multiplicity is how many equivalent points an atom on that site generates in the conventional cell; the general position has the highest multiplicity, equal to the number of operations.
- Site symmetry is the point group that leaves that position fixed; a special position (lower multiplicity) sits on a symmetry element — press + on a row to see its atoms land on the drawn elements.