Pair intersections of the symmetry point groups

The shape of the crystal depends not only on its internal structure, but also on the external conditions that can be both isotropic (chemical composition, temperature, etc.) and anisotropic (heterogeneous matrix, oriented stress, etc.). In the latter case, the inhomogeneous character of the medium can be described, for example, in terms of the Curie limit groups. There is a more specific case - the growth of one crystal inside the other. As a result the shape of crystalline inclusion shows the action both internal medium and external one. The question of the diversity of the external symmetry of crystals growing in crystalline media was first posed and solved by I. I. Shafranovsky for several specific cases. In this paper the solution of the Shafranovsky problem is given. The complete table of variety of external symmetry of crystalline inclusion inside monocrystalline matrix was obtained.