Crystal Lab › The 230 space groups › Tetragonal
No. 89 P 4 2 2
Tetragonal space group · 8 symmetry operations per cell · 16 Wyckoff positions · 2 settings
Symmetry elements and Wyckoff positions (interactive)
No. 89 P 4 2 2
SettingLoading the group…
x = 0.10, y = 0.17, z = 0.08
- Number
- 89
- Hermann–Mauguin symbol
- P 4 2 2
- Hall symbol
P 4 2- Crystal system
- Tetragonal
- Operations per cell
- 8
- General position
- 8p (site symmetry 1)
Wyckoff positions (standard setting)
| Multiplicity | Letter | Site symmetry |
|---|---|---|
| 8 | p | 1 |
| 4 | o | .2. |
| 4 | n | .2. |
| 4 | m | .2. |
| 4 | l | .2. |
| 4 | k | ..2 |
| 4 | j | ..2 |
| 4 | i | 2.. |
| 2 | h | 4.. |
| 2 | g | 4.. |
| 2 | f | 222 . |
| 2 | e | 222 . |
| 1 | d | 422 |
| 1 | c | 422 |
| 1 | b | 422 |
| 1 | a | 422 |
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.