Deriving formulas for calculating the faces of the original belt using the zonal calculation system

Abstract

The geometric constants, even for a triclinic crystal, are five angles, the values of which can be easily determined by direct measurement on a universal goniometer, and then no preliminary calculations are needed; using these same five angular values, using the basic formula, the determination of any face, not only measured, but and every possible one, given by the indices of the symbol, is produced, as mentioned, by simple additions and subtractions, but with the exception of the faces located in the original belt itself, that is, the belt of faces a and b. And in the textbook (“A Brief Course in Crystallography”) there is no formulas are given for calculating the angles between the faces in this belt. Here I will give the derivation of this remarkable and extremely simple formula.