CRYSTALLOGRAPHY, GEOMETRY AND PHYSICS IN HIGHER DIMENSIONS .13. TRI-INCOMMENSURATE CRYSTAL PHASES

This paper and the following one [paper XIV; Weigel & Veysseyre (1994) . Acta Cryst. A50, 444 450] are the fourth and fifth of a series devot ed to incommensurate structures; they deal with the tri-incommensurate crystal phases. Owing to physical considerations for the vectors of m odulation, the tri-incommensurate point-symmetry operations are define d and listed as well as the tri-incommensurate point-symmetry groups a nd the tri-incommensurate crystal families of Euclidean space E6. The first of these two papers mainly consists of the study of the tri-inco mmensurate point-symmetry operations; therefore, some properties of th e point-symmetry operations of Euclidean space E6 are given. The secon d paper is devoted to the mono-, di- and tri-incommensurate point-symm etry groups and crystal families. Finally, a comparison between mono-, di- and tri-incommensurate structures is established.