R-3m (166) Space Group

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Table 3007. R-3m (166) space group.

Name in the International Tables for Crystallography	R-3m	Lattice type	R
Patterson space group	166	Point group	-3m
Crystal system	Trigonal	Laue class	-3m
Number of symmetry operators	36	Example of forbidden reflections in electron diffraction patterns	{1 -1 0 0} reflections
Asymm	0 ≤ x ≤ 2/3 and 0 ≤ y ≤ 2/3 and 0 ≤ z ≤ 1/6 and x ≤ 2 y and y ≤ min(1-x,2 x)
Symmetry (atomic coordinates)	X, Y, Z; -Y, X-Y, Z; Y-X, -X, Z; Y, X, -Z; X-Y, -Y, -Z; -X, Y-X, -Z; -X, -Y, -Z; Y, Y-X, -Z; X-Y, X, -Z; -Y, -X, Z; Y-X, Y, Z; X, X-Y, Z; 2/3+X, 1/3+Y, 1/3+Z; 2/3-Y, 1/3+X-Y, 1/3+Z; 2/3+Y-X, 1/3-X, 1/3+Z; 2/3+Y, 1/3+X, 1/3-Z; 2/3+X-Y, 1/3-Y, 1/3-Z; 2/3-X, 1/3+Y-X, 1/3-Z; 2/3-X, 1/3-Y, 1/3-Z; 2/3+Y, 1/3+Y-X, 1/3-Z; 2/3+X-Y, 1/3+X, 1/3-Z; 2/3-Y, 1/3-X, 1/3+Z; 2/3+Y-X, 1/3+Y, 1/3+Z; 2/3+X, 1/3+X-Y, 1/3+Z; 1/3+X, 2/3+Y, 2/3+Z; 1/3-Y, 2/3+X-Y, 2/3+Z; 1/3+Y-X, 2/3-X, 2/3+Z; 1/3+Y, 2/3+X, 2/3-Z; 1/3+X-Y, 2/3-Y, 2/3-Z; 1/3-X, 2/3+Y-X, 2/3-Z; 1/3-X, 2/3-Y, 2/3-Z; 1/3+Y, 2/3+Y-X, 2/3-Z; 1/3X-Y, 2/3+X, 2/3-Z; 1/3-Y, 2/3-X, 2/3+Z; 1/3+Y-X, 2/3+Y, 2/3+Z; 1/3+X, 2/3+X-Y, 2/3+Z
Crystal examples	K₃H(SeO₄)₂: Parelastic & paraelectric. Rb₃H(SeO₄)₂: Parelastic.

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