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Symmetry in Crystallography$
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Paolo Radaelli

Print publication date: 2011

Print ISBN-13: 9780199550654

Published to Oxford Scholarship Online: December 2013

DOI: 10.1093/acprof:oso/9780199550654.001.0001

The 14 3D Bravais lattices

Chapter:
(p.83) 9 The 14 3D Bravais lattices
Source:
Symmetry in Crystallography
Author(s):

Paolo G. Radaelli

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199550654.003.0009

This chapter constructs all the possible 3D translation sets compatible with the previously introduced 3D point groups, leading to the well-known fourteen Bravais lattices. For each crystal system, the compatible lattices (both primitive and centred) are defined, together with the corresponding holohedry (lattice symmetry). The more complex centred lattices, such as the R-centred trigonal lattice, receive particular attention. A reference is made to the different unit cell conventions (with a particular note about the monoclinic system), although this is too intricate a subject for such an introductory level textbook.

Keywords:   holohedry, Bravais lattices, crystal system

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