Abstract
In this chapter, reduced bases (reduced cells) are described. The treatment starts with the definition of the reduced basis and the reduced form in terms of the metric tensor and lists the conditions (both main and special) for reduced bases of type-I cells and type-II cells. This is followed by a detailed and systematic geometric explanation of these conditions. The resulting 44 lattice characters are defined and tabulated, and the relations between the lattice characters and the conventional cell parameters of the 14 Bravais lattices are listed and discussed. This chapter is also available as HTML from the International Tables Online site hosted by the IUCr.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 International Union of Crystallography
About this entry
Cite this entry
de Wolff, P.M. (2006). Reduced bases. In: Hahn, T. (eds) International Tables for Crystallography Volume A: Space-group symmetry. International Tables for Crystallography, vol A. Springer, Dordrecht. https://doi.org/10.1107/97809553602060000518
Download citation
DOI: https://doi.org/10.1107/97809553602060000518
Publisher Name: Springer, Dordrecht
Print ISBN: 978-0-7923-6590-7
Online ISBN: 978-1-4020-5406-8
eBook Packages: Springer Book Archive