CRYSTALLOGRAPHY, GEOMETRY AND PHYSICS IN HIGHER DIMENSIONS .14. FILIATION FROM ONE-DIMENSIONAL, 2-DIMENSIONAL AND 3-DIMENSIONAL CRYSTAL FAMILIES AND POINT GROUPS TO THE MONOINCOMMENSURATE, DI-INCOMMENSURATE AND TRI-INCOMMENSURATE CRYSTAL FAMILIES IN 4-DIMENSIONAL, 5-DIMENSIONAL AND 6-DIMENSIONAL SPACES

Citation
D. Weigel et R. Veysseyre, CRYSTALLOGRAPHY, GEOMETRY AND PHYSICS IN HIGHER DIMENSIONS .14. FILIATION FROM ONE-DIMENSIONAL, 2-DIMENSIONAL AND 3-DIMENSIONAL CRYSTAL FAMILIES AND POINT GROUPS TO THE MONOINCOMMENSURATE, DI-INCOMMENSURATE AND TRI-INCOMMENSURATE CRYSTAL FAMILIES IN 4-DIMENSIONAL, 5-DIMENSIONAL AND 6-DIMENSIONAL SPACES, Acta crystallographica. Section A, Foundations of crystallography, 50, 1994, pp. 444-450
Citations number
7
Categorie Soggetti
Crystallography
ISSN journal
01087673
Volume
50
Year of publication
1994
Part
4
Pages
444 - 450
Database
ISI
SICI code
0108-7673(1994)50:<444:CGAPIH>2.0.ZU;2-T
Abstract
The previous paper in this series [Phan & Veysseyre (1994). Acta Cryst . A50, 438-444] mainly compared the mono-, di- and tri-incommensurate point-symmetry operations, their number and their symbols. In this pap er, the filiation from the gZ-irreducible crystal families of the one- , two- and three-dimensional spaces to the mono-, di- and tri-incommen surate families of the four-, five- and six-dimensional spaces is esta blished. The holohedries and the different point groups of these cryst al families are compared. The paper begins with a list of the incommen surate families; then a series of nine further tables establishes the connection between the different families and their point groups. It i s proved that there are 30 mono-incommensurate (MI) point groups, 47 d i-incommensurate (DI) point groups and 57 tri-incommensurate (TI) poin t groups belonging to the six MI crystal families of four-dimensional space, to the 11 DI crystal families of five-dimensional space and to the 14 TI crystal families of the six-dimensional space.