International
Tables for
Crystallography
Volume A
Space-group symmetry
Edited by M. I. Aroyo

International Tables for Crystallography (2015). Vol. A, ch. 1.5, p. 88

Figure 1.5.3.3 

G. Chapuis,d H. Wondratscheka and M. I. Aroyob
[Figure 1.5.3.3]
Figure 1.5.3.3

General-position diagram of the space group R3m (160) showing the relation between the hexagonal and rhombohedral axes in the obverse setting: [{\bf a}_{\rm rh}] = [\textstyle{{1}\over{3}}(2{\bf a}_{\rm hex}+{\bf b}_{\rm hex}+{\bf c}_{\rm hex})], [{\bf b}_{\rm rh}] = [\textstyle{{1}\over{3}}(-{\bf a}_{\rm hex}+{\bf b}_{\rm hex}+{\bf c}_{\rm hex})], [{\bf c}_{\rm rh}] = [\textstyle{{1}\over{3}}(-{\bf a}_{\rm hex}] [-2{\bf b}_{\rm hex}+{\bf c}_{\rm hex})].