Crystal Lab › The 230 space groups › Tetragonal
No. 123 P 4/m m m
Tetragonal space group · 16 symmetry operations per cell · 21 Wyckoff positions · 2 settings
Symmetry elements and Wyckoff positions (interactive)
No. 123 P 4/m m m
SettingLoading the group…
x = 0.10, y = 0.17, z = 0.08
- Number
- 123
- Hermann–Mauguin symbol
- P 4/m m m
- Hall symbol
-P 4 2- Crystal system
- Tetragonal
- Operations per cell
- 16
- General position
- 16u (site symmetry 1)
Wyckoff positions (standard setting)
| Multiplicity | Letter | Site symmetry |
|---|---|---|
| 16 | u | 1 |
| 8 | t | .m. |
| 8 | s | .m. |
| 8 | r | ..m |
| 8 | q | m.. |
| 8 | p | m.. |
| 4 | o | m2m . |
| 4 | n | m2m . |
| 4 | m | m2m . |
| 4 | l | m2m . |
| 4 | k | m.2 m |
| 4 | j | m.2 m |
| 4 | i | 2mm . |
| 2 | h | 4mm |
| 2 | g | 4mm |
| 2 | f | mmm . |
| 2 | e | mmm . |
| 1 | d | 4/mmm |
| 1 | c | 4/mmm |
| 1 | b | 4/mmm |
| 1 | a | 4/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.