International
Tables for Crystallography Volume A Spacegroup symmetry Edited by Th. Hahn © International Union of Crystallography 2006 
International Tables for Crystallography (2006). Vol. A, ch. 4.3, pp. 7173

In the 1935 edition of International Tables, for each tetragonal P and I space group an additional Ccell and Fcell description was given. In the corresponding spacegroup symbols, secondary and tertiary symmetry elements were simply interchanged. Coordinate triplets for these larger cells were not printed, except for the space groups of class . In IT (1952), the C and F cells were dropped from the spacegroup tables but kept in the comparative tables.
In the present edition, the C and F cells reappear in the sub and supergroup tabulations of Part 7 , as well as in the synoptic Table 4.3.2.1, where short and extended (twoline) symbols are given for P and C cells, as well as for I and F cells.
In the crystal classes 42(2), 4m(m), or , , where the tertiary symmetry elements are between parentheses, one finds Analogous relations hold for the space groups. In order to have the symmetry direction of the tertiary symmetry elements along [] (cf. Table 2.2.4.1 ), one has to choose the primary and secondary symmetry elements in the product rule along [001] and [010].
Example
In , one has so that would be the short symbol. In fact, in IT (1935), the tertiary symmetry element was suppressed for all groups of class 422, but reestablished in IT (1952), the main reason being the generation of the fourfold rotation as the product of the secondary and tertiary symmetry operations: etc.
As a result of periodicity, in all space groups of classes 422, and , the two tertiary diagonal axes 2, along [] and [110], alternate with axes , the screw component being , 0 (cf. Table 4.1.2.2 ).
Likewise, tertiary diagonal mirrors m in x, x, z and in space groups of classes 4mm, and alternate with glide planes called g,^{1} the glide components being , , 0. The same glide components produce also an alternation of diagonal glide planes c and n (cf. Table 4.1.2.2 ).
The transformations from the P to the two C cells, or from the I to the two F cells, are (cf. Fig. 5.1.3.5 ). The secondary and tertiary symmetry directions are interchanged in the double cells. It is important to know how primary, secondary and tertiary symmetry elements change in the new cells .

Examples are given for maximal k subgroups of P groups (i), of I groups (ii), and for maximal tetragonal, orthorhombic and monoclinic t subgroups.

References
Internationale Tabellen zur Bestimmung von Kristallstrukturen (1935). 1. Band, edited by C. Hermann. Berlin: Borntraeger. [Revised edition: Ann Arbor: Edwards (1944). Abbreviated as IT (1935).]International Tables for Xray Crystallography (1952). Vol. I, edited by N. F. M. Henry & K. Lonsdale. Birmingham: Kynoch Press. [Abbreviated as IT (1952).]