Crystal Lab › The 230 space groups › Trigonal
No. 167 R -3 c :h
Trigonal space group · 36 symmetry operations per cell · 6 Wyckoff positions · 2 settings
Symmetry elements and Wyckoff positions (interactive)
No. 167 R -3 c :h
SettingLoading the group…
x = 0.10, y = 0.17, z = 0.08
- Number
- 167
- Hermann–Mauguin symbol
- R -3 c :h
- Hall symbol
-R 3 2"c- Crystal system
- Trigonal
- Operations per cell
- 36
- General position
- 36f (site symmetry 1)
Wyckoff positions (standard setting)
| Multiplicity | Letter | Site symmetry |
|---|---|---|
| 36 | f | 1 |
| 18 | e | .2 |
| 18 | d | -1 |
| 12 | c | 3. |
| 6 | b | -3. |
| 6 | a | 32 |
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
- Corundum (Al₂O₃) — A₂B₃
- Calcite (CaCO₃) — Carbonate
- NASICON (Na₃Zr₂Si₂PO₁₂) — Framework ionic conductor