PARALLEL EMBEDDING OF POLYHEDRONS AND EFFICIENT USE OF NATURAL DIAMONDS
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PARALLEL EMBEDDING OF POLYHEDRONS AND EFFICIENT USE OF NATURAL DIAMONDS
Annotation
PII
S042473880000616-6-1
Publication type
Article
Status
Published
Authors
Lev Babat 
Alexander Fridman
Pages
54-63
Abstract

The embedding of pairs of intersecting proper n-dimensional simplexes is studied. Simplex A is embedded parallel in simplex B if the outer normals of A and B are unidirectional. Their pairs are said to be embedded parallel if one pair simplexes are embedded parallel into another pair simplexes. Each pair is associated with n + 3 parameters. Theorem: a pair A or its mirror image is embedded parallel in pair B if and only in case parameters of A do not exceed parameters of B. The theorem is used for the analysis of effi cient use of raw diamonds.

Keywords
outer normal, mirror image, star, parallel embedding, regular simplex
Date of publication
01.07.2015
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0
Views
111
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References



Additional sources and materials

Babat L.G. (2008). Issledovanie stereotipov stoimostnoj otsenki almazov. M.: TsEhMI RAN.

Babat L.G. (2010). Oktaehdricheskie almazy i ε-optimal'nye kruglye brillianty. M.: TsEhMI RAN.

Babat L.G., Fridman A.A. (2008). Parallel'nye vlozheniya mnogogrannikov // Diskretnaya matematika. T. 20. № 2. S. 122–159.

Fridman A.A. (2011). Problemy ehffektivnogo ispol'zovaniya prirodnykh almazov: sovremennyj kontekst // Ehkonomika i matematicheskie metody. T. 47. № 3. S. 41–55.