Crystal Lab › The 17 plane groups › Hexagonal
No. 15 p31m
Hexagonal plane group · 6 symmetry operations per cell · 4 Wyckoff positions
Symmetry elements and Wyckoff positions (interactive)
No. 15 p31m
SettingLoading the group…
x = 0.10, y = 0.17, z = 0.08
- Number
- 15
- Hermann–Mauguin symbol
- p31m
- Lattice
- Hexagonal
- Operations per cell
- 6
- General position
- 6d (site symmetry 1)
Wyckoff positions (standard setting)
| Multiplicity | Letter | Site symmetry |
|---|---|---|
| 6 | d | 1 |
| 3 | c | ..m |
| 2 | b | 3.. |
| 1 | a | 3.m |
How to read it
- Each symmetry element drawn in the cell is worked out from the group’s operations. This is a two-dimensional group, so there are only rotation points and mirror or glide lines: rotation points are small filled shapes marked with their order (2, 3, 4 or 6), and mirror and glide lines run across the cell (dashed outline = glide). 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.