Geodesic
Volume polynomial for polyhedra of hexahedral type
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 1078-1087.

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

We present an algorithm for the explicit construction of the canonical volume polynomials for polyhedra combinatorially isomorphic to a hexahedron and realize them in the case of some special values of edge lengths.
Keywords: hexahedral-type polyhedra
Mots-clés : volume, polynomial equation. 
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D. I. Sabitov; I. Kh. Sabitov. Volume polynomial for polyhedra of hexahedral type. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 1078-1087. http://geodesic.mathdoc.fr/item/SEMR_2017_14_a64/

[1] Sabitov I. Kh., “The volume of a polyhedron as a function of its metric”, Fundam. and applied mathematics, 2:4 (1996), 1235–1246 (Russian) | MR | Zbl

[2] Sb. Math., 189:9–10 (1998), 1533–1561 | DOI | MR | Zbl

[3] Sabitov I. Kh., “The volume as a metric invariant of polyhedra”, Discrete and Computatioal Geometry, 20:4 (1998), 405–425 | DOI | MR | Zbl

[4] Russian Math. Surveys, 66:3 (2011), 445–505 | DOI | DOI | MR | Zbl

[5] Russian Math. Surveys, 54:2 (1999), 430–431 | DOI | DOI | MR | Zbl

[6] Russian Math. Surveys, 50:5 (1995), 1085–1087 | DOI | MR | Zbl

[7] Math. Notes, 76:1–2 (2004), 25–40 | DOI | DOI | MR | Zbl

[8] Sabitov D. I., Sabitov I. Kh., “Volume polynomials for some polyhedra in spaces of constant curvature”, Modeling and analysis of of information systems, 19:6 (2012), 159–167 | MR