Crystal Lab › The 230 space groups › Tetragonal
No. 139 I 4/m m m
Tetragonal space group · 32 symmetry operations per cell · 15 Wyckoff positions · 2 settings
Symmetry elements and Wyckoff positions (interactive)
No. 139 I 4/m m m
SettingLoading the group…
x = 0.10, y = 0.17, z = 0.08
- Number
- 139
- Hermann–Mauguin symbol
- I 4/m m m
- Hall symbol
-I 4 2- Crystal system
- Tetragonal
- Operations per cell
- 32
- General position
- 32o (site symmetry 1)
Wyckoff positions (standard setting)
| Multiplicity | Letter | Site symmetry |
|---|---|---|
| 32 | o | 1 |
| 16 | n | .m. |
| 16 | m | ..m |
| 16 | l | m.. |
| 16 | k | ..2 |
| 8 | j | m2m . |
| 8 | i | m2m . |
| 8 | h | m.2 m |
| 8 | g | 2mm . |
| 8 | f | ..2/m |
| 4 | e | 4mm |
| 4 | d | -4m2 |
| 4 | c | mmm . |
| 2 | b | 4/mmm |
| 2 | a | 4/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.
Crystal Lab structures in this group
- Potassium nickel fluoride (K₂NiF₄) — Layered perovskite (Ruddlesden–Popper n = 1)
- Thallium cuprate Tl-2223 (superconductor) (Tl₂Ba₂Ca₂Cu₃O₁₀) — Layered cuprate (triple CuO₂ layers)
Prototype structures in this group (51)
Ge₁₀Ho₁₁O₁₀Sr₄Ti₃Mn₁₂Th D2bCo₂S₂TlCr₂Si₂ThAs₂Mn₃O₂Sr₂Au₂Nb₃ClO₅Sc₂Sr₃Al₂Ge₈Sc₁₁Cl₂CuO₂Sr₂Ba₂CaCu₂O₈Sr₂B₂CLuNi₂H₂Th L'2bC₂Ca C11aBa₃Ge₁₆Ir₄Ca₃Cl₂Cu₂O₄Al₃Zr D023Al₃Ti D022As₄Ca₂F₂Fe₄KAs₄Ba₂Fe₂OTi₂Cl₄K₂O₂Os J15F₄K₂NiNd₄Ni₃O₈Cu₄Ti₃V₄Zn₅Al₄Ba D13Bi₄O₁₁V₂Cl₆(H₂O)₂K₃Tl J31In₆Si₄Tb₁₁Cl₇Mn₂Rb₃O₇Sr₃Ti₂Fe₈N D2gPt₈TiCLi₂N₂Ca(H₂O)_{10.5}(PO₄)₂(UO₂)₂ H59HgNa₂O₂CuNd₂O₄Ba₂CuO₄BaSb₂ZnReSi₂MoSi₂ C11bAuCl₃Cs K76BaBi₄O₁₅Ti₄CeIn₇Pt₂C_{x}Fe L'20FeLiO₂ClHg D31In A6Pa AaSiC