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Diskr. Mat., 2008, Volume 20, Issue 2, Pages 122–159 (Mi dm1007)  

This article is cited in 1 scientific paper (total in 1 paper)

Parallel embeddings of octahedral polyhedra

L. G. Babat, A. A. Fridman


Abstract: 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.

DOI: https://doi.org/10.4213/dm1007

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English version:
Discrete Mathematics and Applications, 2008, 18:3, 301–340

Bibliographic databases:

UDC: 519.2
Received: 20.10.2006
Revised: 22.03.2007

Citation: L. G. Babat, A. A. Fridman, “Parallel embeddings of octahedral polyhedra”, Diskr. Mat., 20:2 (2008), 122–159; Discrete Math. Appl., 18:3 (2008), 301–340

Citation in format AMSBIB
\Bibitem{BabFri08}
\by L.~G.~Babat, A.~A.~Fridman
\paper Parallel embeddings of octahedral polyhedra
\jour Diskr. Mat.
\yr 2008
\vol 20
\issue 2
\pages 122--159
\mathnet{http://mi.mathnet.ru/dm1007}
\crossref{https://doi.org/10.4213/dm1007}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2450037}
\zmath{https://zbmath.org/?q=an:1182.52011}
\elib{http://elibrary.ru/item.asp?id=20730247}
\transl
\jour Discrete Math. Appl.
\yr 2008
\vol 18
\issue 3
\pages 301--340
\crossref{https://doi.org/10.1515/DMA.2008.023}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-47249127785}


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  • https://doi.org/10.4213/dm1007
  • http://mi.mathnet.ru/eng/dm/v20/i2/p122

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Fridman A.A., “Problemy effektivnogo ispolzovaniya prirodnykh almazov: sovremennyi kontekst”, Ekonomika i matematicheskie metody, 47:3 (2011), 41–55  mathscinet  elib
  • Дискретная математика
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