Geodesic
Parallel embeddings of octahedral polyhedra
Diskretnaya Matematika, Tome 20 (2008) no. 2, pp. 122-159.

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
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L. G. Babat; A. A. Fridman. Parallel embeddings of octahedral polyhedra. Diskretnaya Matematika, Tome 20 (2008) no. 2, pp. 122-159. http://geodesic.mathdoc.fr/item/DM_2008_20_2_a8/

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