No. 166 R -3 m :h

Number

166

Hermann–Mauguin symbol

R -3 m :h

Hall symbol

-R 3 2"

Crystal system

Trigonal

Operations per cell

36

General position

36i (site symmetry 1)

Wyckoff positions (standard setting)

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

• Cadmium chloride (CdCl₂) — Layered AB₂, 6:3
• Lithium cobalt oxide (layered) (LiCoO₂) — Layered rock-salt (α-NaFeO₂ type)
• Bismuth selenide (Bi₂Se₃) — Layered chalcogenide
• Niobium disulfide (3R) (NbS₂) — Layered AB₂ (trigonal prismatic)

Prototype structures in this group (75)

B₁₃C₂ D1gP₄Sn₃Be₁₇Nb₂Th₂Zn₁₇Cl₂Cu₃H₆O₆ZnBi₂Te₃ C33Fe₂O₄YbBi₂STe₂Bi₂MnTe₄BCTh₂La₃Mn₂O₁₄Sb₃Ni₃Pb₂S₂Ba₃Cr₂O₈C₂TaVFe₃Sn₂Cu₃K₃P₂In₃Te₄P₃Sn₄Fe₄GeTe₂Be₃NbSn₃SrAl₃HoP₃SnAl₄C₃ D71Bi₄Te₃Ce₄Ga₅Rh₉Ba₄NbO₁₂Ru₃Al₄AuCeGe₂Ce₅Co₁₉Al_{3.8}Ca_{1.4}H₂₆O₃₇Si_{8.3}Sr_{0.3} S34(I)B₅Mo₂ D8iCe₅Ga₇Rh₁₂Al₆C₃N₂Bi₆MnTe₁₀CaC₆Ce₇Ga₁₁Rh₁₈Co₇Er₂Fe₇W₆ D85Cl₈Mn₃Na₂Al₈C₃N₄Li₈Pb₂GeSb₂Te₄CdCl₂CaSi₂ C12GaRh₃Y₂BaO₃RuBaPb₃CuS₄Ti₂CaCu₄P₂CaO₄UAlF₆K₂LiCsSb₆V₆TaTi₇CrNaS₂ F51CuFeO₂FeNaO₂LiNiO₂Li₂Mn₃O₇KNO₃ISSmFOYCuPt L11HKS B22ClZrBrZrHf₃N₂Hf₄N₃BBPo AiHg A10As A7COSm C19