MODELING CRYSTAL GROWTH: POLYHEDRA WITH FACES PARALLEL TO PLANES FROM A FIXED FINITE SET.

In this paper we present growing crystal as a point in finite dimentional space moving inside a cone SG ⊂ ℝm corresponding to the family BG of polyhedra with faces parallel to planes from a fixed finite set G. For this purpose we modify Minkowski addition of convex sets and explain in depth a representation of a growth of certain crystal of NaCl. We also provide a number of illustrations of a respective cone S'G of symmetric polyhedra and the trajectory of our growing crystal which is a broken line. [ABSTRACT FROM AUTHOR]