Crystal Lab › The 230 space groups › Cubic
No. 221 P m -3 m
Cubic space group · 48 symmetry operations per cell · 14 Wyckoff positions
Symmetry elements and Wyckoff positions (interactive)
No. 221 P m -3 m
SettingLoading the group…
x = 0.10, y = 0.17, z = 0.08
- Number
- 221
- Hermann–Mauguin symbol
- P m -3 m
- Hall symbol
-P 4 2 3- Crystal system
- Cubic
- Operations per cell
- 48
- General position
- 48n (site symmetry 1)
Wyckoff positions (standard setting)
| Multiplicity | Letter | Site symmetry |
|---|---|---|
| 48 | n | 1 |
| 24 | m | ..m |
| 24 | l | m.. |
| 24 | k | m.. |
| 12 | j | m.m 2 |
| 12 | i | m.m 2 |
| 12 | h | mm2 . . |
| 8 | g | .3m |
| 6 | f | 4m. m |
| 6 | e | 4m. m |
| 3 | d | 4/mm. m |
| 3 | c | 4/mm. m |
| 1 | b | m-3m |
| 1 | a | m-3m |
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
- Simple cubic (Po) — Elemental
- Caesium chloride (CsCl) — AB, 8:8
- Perovskite (ideal cubic) (SrTiO₃) — ABO₃
- Rhenium trioxide (ReO₃) — AB₃