The Seven Crystal Systems

Abstract

In the various lattices, the vectors $\overrightarrow a ,\;\overrightarrow b \;{\text{and}}\;\overrightarrow c$ must be chosen and associated with a system of suitable crystallographic axes, a, b, c. This is not done arbitrarily. Generally, so far as is possible, the choices are made so that the direction of rotation axes, rotoinversion axes and the normals to mirror planes are parallel to $\overrightarrow a ,\;\overrightarrow b {\text{,}}\;\overrightarrow c$ and to a, b, c:

$$ \overrightarrow a ,\;\overrightarrow b ,\;\overrightarrow c ;\;a,b,c\;{\text{//}}\;X,\;\overline X ,\;normal\;to\;m $$

((99.1))

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