International
Tables for
Crystallography
Volume A
Space-group symmetry
Edited by Th. Hahn

© International Union of Crystallography 2006
International Tables for Crystallography (2006). Vol. A. ch. 5.1, p. 84

Figure 5.1.3.6 

H. Arnolda‡

a Institut für Kristallographie, Rheinisch-Westfälische Technische Hochschule, Aachen, Germany

[Figure 5.1.3.6]
Figure 5.1.3.6

Unit cells in the rhombohedral lattice: same origin for all cells. The basis of the rhombohedral cell is labelled a, b, c. Two settings of the triple hexagonal cell are possible with respect to a primitive rhombohedral cell: The obverse setting with the lattice points 0, 0, 0; [{2 \over 3}, {1 \over 3}, {1 \over 3}]; [{1 \over 3}, {2 \over 3}, {2 \over 3}] has been used in International Tables since 1952. Its general reflection condition is [- h + k + l = 3n]. The reverse setting with lattice points 0, 0, 0; [{1 \over 3}, {2 \over 3}, {1 \over 3}]; [{2 \over 3}, {1 \over 3}, {2 \over 3}] was used in the 1935 edition. Its general reflection condition is [h - k + l = 3n]. (a) Obverse setting of triple hexagonal cell [a_{1},b_{1},c_{1}] in relation to the primitive rhombohedral cell a, b, c. (b) Reverse setting of triple hexagonal cell [a_{2},b_{2},c_{2}] in relation to the primitive rhombohedral cell a, b, c.­(c) Primitive rhombohedral cell (- - - lower edges), a, b, c in relation to the three triple hexagonal cells in obverse setting [a_{1},b_{1},c']; [a_{2},b_{2},c'];­[a_{3},b_{3},c']. Projection along c′. (d) Primitive rhombohedral cell (- - - lower edges), a, b, c in relation to the three triple hexagonal cells in reverse setting [a_{1},b_{1},c']; [a_{2},b_{2},c']; [a_{3},b_{3},c']. Projection along c′.