Crystal Lab › The 230 space groups › Tetragonal
No. 141 I 41/a m d :2
Tetragonal space group · 32 symmetry operations per cell · 9 Wyckoff positions · 4 settings
Symmetry elements and Wyckoff positions (interactive)
No. 141 I 41/a m d :2
SettingLoading the group…
x = 0.10, y = 0.17, z = 0.08
- Number
- 141
- Hermann–Mauguin symbol
- I 41/a m d :2
- Hall symbol
-I 4bd 2- Crystal system
- Tetragonal
- Operations per cell
- 32
- General position
- 32i (site symmetry 1)
Wyckoff positions (standard setting)
| Multiplicity | Letter | Site symmetry |
|---|---|---|
| 32 | i | 1 |
| 16 | h | .m. |
| 16 | g | ..2 |
| 16 | f | .2. |
| 8 | e | 2mm . |
| 8 | d | .2/m. |
| 8 | c | .2/m. |
| 4 | b | -4m2 |
| 4 | a | -4m2 |
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
- Anatase (TiO₂) — AB₂, 6:3