Crystal Lab › The 230 space groups › Hexagonal
No. 191 P 6/m m m
Hexagonal space group · 24 symmetry operations per cell · 18 Wyckoff positions
Symmetry elements and Wyckoff positions (interactive)
No. 191 P 6/m m m
SettingLoading the group…
x = 0.10, y = 0.17, z = 0.08
- Number
- 191
- Hermann–Mauguin symbol
- P 6/m m m
- Hall symbol
-P 6 2- Crystal system
- Hexagonal
- Operations per cell
- 24
- General position
- 24r (site symmetry 1)
Wyckoff positions (standard setting)
| Multiplicity | Letter | Site symmetry |
|---|---|---|
| 24 | r | 1 |
| 12 | q | m.. |
| 12 | p | m.. |
| 12 | o | .m. |
| 12 | n | ..m |
| 6 | m | mm2 |
| 6 | l | mm2 |
| 6 | k | m2m |
| 6 | j | m2m |
| 6 | i | 2mm |
| 4 | h | 3m. |
| 3 | g | mmm |
| 3 | f | mmm |
| 2 | e | 6mm |
| 2 | d | -6m2 |
| 2 | c | -6m2 |
| 1 | b | 6/mmm |
| 1 | a | 6/mmm |
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.
Crystal Lab structures in this group
- Lithium nitride (Li₃N) — Layered ionic conductor