Crystal Lab › The 230 space groups › Cubic
No. 227 F d -3 m :2
Cubic space group · 192 symmetry operations per cell · 9 Wyckoff positions · 2 settings
Symmetry elements and Wyckoff positions (interactive)
No. 227 F d -3 m :2
SettingLoading the group…
x = 0.10, y = 0.17, z = 0.08
- Number
- 227
- Hermann–Mauguin symbol
- F d -3 m :2
- Hall symbol
-F 4vw 2vw 3- Crystal system
- Cubic
- Operations per cell
- 192
- General position
- 192i (site symmetry 1)
Wyckoff positions (standard setting)
| Multiplicity | Letter | Site symmetry |
|---|---|---|
| 192 | i | 1 |
| 96 | h | ..2 |
| 96 | g | ..m |
| 48 | f | 2.m m |
| 32 | e | .3m |
| 16 | d | .-3m |
| 16 | c | .-3m |
| 8 | b | -43m |
| 8 | a | -43m |
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
- Diamond (C) — Covalent network
- Spinel (MgAl₂O₄) — AB₂O₄
- Magnetite (inverse spinel) (Fe₃O₄) — Inverse spinel AB₂O₄
- Lithium manganese oxide (spinel) (LiMn₂O₄) — Spinel cathode
- Faujasite (zeolite X/Y) (Na₅₆(Al,Si)₁₉₂O₃₈₄) — Zeolite framework