Geodesic
Parallel embeddings of octahedral polyhedra
Diskretnaya Matematika, Tome 20 (2008) no. 2, pp. 122-159 
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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     title = {Parallel embeddings of octahedral polyhedra},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2008_20_2_a8/}
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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.

[1] Fridman A. A., Babat L. G., Mirovoi almazobrilliantovyi rynok. Matematicheskie aspekty otsenki i obrabotki almazov, TsEMI RAN, Moskva, 1995

[2] Fridman A. A., Babat L. G., Mirovoi almazobrilliantovyi rynok. Matematicheskii metod otsenki i obrabotki almazov, TsEMI RAN, Moskva, 1995

[3] Fridman A. A., Babat L. G., Mirovoi almazobrilliantovyi rynok. Issledovanie vliyaniya formy almaza na ego stoimost: matematicheskii podkhod i kompyuternaya realizatsiya, TsEMI RAN, Moskva, 1996

[4] Fridman A. A., Babat L. G., Optimalnoe vlozhenie brillianta v almaz i stoimostnaya otsenka almaza, TsEMI RAN, Moskva, 2005

[5] Strodiot J., Nguyen Van Hien, Nguyen Van Thoai, “Application of nonsmooth optimization to a design: Centering problem”, Spetsialnyi otchet Mezhdunarodnogo instituta sistemnogo analiza, 1985