# Orthogonal rate and form development

The growth of a face is characterized by its growth rate to the face in question. This is the orthogonal rate R of the face.

Now let us consider two faces A and B that intersect along edge O, examining the rate R on a plane perpendicular to this edge.

**Figure 1.1. ***Development of crystal faces*

The orthogonal growth of faces A and B are, respectively, Om and On with, as in the figure:

We can see that face A has increased its surface by mO', whereas face B has lostnO'. The edge has moved from O to O'.

Face A becomes *important* and, after sufficient time, face B will disappear, thereby becoming a *virtual* face. Corresponding with the growth progression of the crystal, the number of faces decreases, becoming simpler in form. *Important faces have the lowest orthogonal rates.*

Here, we can introduce the concept of a face’s *morphological importance *(MI) as the statistical mean of a face’s surface compared with the mean of the crystals’ total exterior surface. It is consistent to establish MI for a crystal population close in size, since their form increasingly varies as size increases.