Geometric elements of crystallography. (Q2771045)

The book deals with an opportune subject -- mathematics in crystallography -- an interface between geology and mathematics, and throughout the manuscript the author keeps in mind that the readers will be from both scientific areas. This preoccupation has a nasty effect on the 1st chapter, dealing with the notions of symmetry and structure, by making it too long and a bit confusing, but fortunately this sort of style disappears in the other chapters, where the subjects are well presented in a simple and accurate language that is appropriate for non-mathematicians, some of the subject's history is introduced and the geology's approach is always emphasized. NEWLINENEWLINENEWLINEThe contents of the book can be described as follows: the 2nd chapter is about the concept of crystal net, dealing with systems of symmetry, geometric elements such as dihedral angles and faces of a crystal and their representation using projection, including some applications to usual problems; the 3rd chapter describes symmetry elements, namely the center of symmetry, symmetry planes, rotation and inversion axes and improper rotation axes and introduces the different notations and some results associated with them; chapter 4 studies symmetry from a group-theoretic point of view and it classifies the symmetry groups in 3-space that fix a point, while the 5th chapter explains how the symmetry reflects on the morphologic properties of a crystal; the translation appears in the 6th chapter, that deals with crystal nets and translational symmetry, including the composion of a translation with a movement that fixes a point; finally, the classification of the 230 crystallographic groups is done in the three remaning chapters.