Parallel embeddings of octahedral polyhedra

We construct a combinatorial representation of an octahedral polyhedron (crystal), find its geometrical parameters, and show that the parameters of such a polyhedron and its mirror image coincide and are simply measured.
Using the combinatorial representation of a diamond, we are able to construct an algorithm which finds a round cut diamond of maximum radius embedded into an octahedral diamond and determines how to place this cut diamond in the octahedral one. This results in creating a technological process to cut round diamonds of maximum value from octahedral ones.