A complete quadrilateral in crystallography and a graphical method for finding complex indices

Abstract

Since in general, to define a complex, four faces are necessary and sufficient, it is clear that with three given points, the vertices of any triangle, their poles constitute, further development of the complex is impossible, and it is absolutely necessary to know the position of some other fourth face. In general, the choice of such depends on our desire, and I will consider the case when these four points form the vertices of two adjacent triangles that have a common side.