Crystal Lab › The 230 space groups › Cubic
No. 208 P 42 3 2
Cubic space group · 24 symmetry operations per cell · 13 Wyckoff positions
Symmetry elements and Wyckoff positions (interactive)
No. 208 P 42 3 2
SettingLoading the group…
x = 0.10, y = 0.17, z = 0.08
- Number
- 208
- Hermann–Mauguin symbol
- P 42 3 2
- Hall symbol
P 4n 2 3- Crystal system
- Cubic
- Operations per cell
- 24
- General position
- 24m (site symmetry 1)
Wyckoff positions (standard setting)
| Multiplicity | Letter | Site symmetry |
|---|---|---|
| 24 | m | 1 |
| 12 | l | ..2 |
| 12 | k | ..2 |
| 12 | j | 2.. |
| 12 | i | 2.. |
| 12 | h | 2.. |
| 8 | g | .3. |
| 6 | f | 2.2 2 |
| 6 | e | 2.2 2 |
| 6 | d | 222 . . |
| 4 | c | .32 |
| 4 | b | .32 |
| 2 | a | 23. |
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.