Crystal Lab › The 80 layer groups › Orthorhombic
No. 47 cmmm
Orthorhombic layer group · 16 symmetry operations per cell · 12 Wyckoff positions
Symmetry elements and Wyckoff positions (interactive)
No. 47 cmmm
SettingLoading the group…
x = 0.10, y = 0.17, z = 0.08
- Number
- 47
- Hermann–Mauguin symbol
- cmmm
- Crystal system
- Orthorhombic
- Operations per cell
- 16
- General position
- 16l (site symmetry 1)
Wyckoff positions (standard setting)
| Multiplicity | Letter | Site symmetry |
|---|---|---|
| 16 | l | 1 |
| 8 | k | ..m |
| 8 | j | .m. |
| 8 | i | m.. |
| 8 | h | ..2 |
| 4 | g | mm2 |
| 4 | f | mm2 |
| 4 | e | m2m |
| 4 | d | 2mm |
| 4 | c | ..2/m |
| 2 | b | mmm |
| 2 | a | 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.