Geodesic
Volume polynomials for polyhedra combinatorially isometric to $n$-prisms in the cases $n=5,6,7$
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 439-448.

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

We present an algorithm for an explicit construction of the canonical volume polynomials for polyhedra combinatorially isomorphic to an $n$-prism in the cases $n=5,6$ and $n=7$ and realize them in the case of some special values of edge lengths.
Keywords: $n$-prism-type polyhedra
Mots-clés : volume, polynomial equation. 
@article{SEMR_2019_16_a52,
     author = {D. I. Sabitov and I. Kh. Sabitov},
     title = {Volume polynomials for polyhedra combinatorially isometric to $n$-prisms in the cases $n=5,6,7$},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {439--448},
     publisher = {mathdoc},
     volume = {16},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2019_16_a52/}
}
TY  - JOUR
AU  - D. I. Sabitov
AU  - I. Kh. Sabitov
TI  - Volume polynomials for polyhedra combinatorially isometric to $n$-prisms in the cases $n=5,6,7$
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2019
SP  - 439
EP  - 448
VL  - 16
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2019_16_a52/
LA  - ru
ID  - SEMR_2019_16_a52
ER  - 
%0 Journal Article
%A D. I. Sabitov
%A I. Kh. Sabitov
%T Volume polynomials for polyhedra combinatorially isometric to $n$-prisms in the cases $n=5,6,7$
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2019
%P 439-448
%V 16
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2019_16_a52/
%G ru
%F SEMR_2019_16_a52
D. I. Sabitov; I. Kh. Sabitov. Volume polynomials for polyhedra combinatorially isometric to $n$-prisms in the cases $n=5,6,7$. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 439-448. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a52/

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

[2] I. Kh. Sabitov, “A generalized Heron–Tataglia formula and some its consequences”, Mathem. sbornik, 189:10 (1998), 105–134 | MR | Zbl

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

[4] A.V. Astrelin, I.Kh. Sabitov, “A canonical polynomial for the volume of a polyheron”, Uspekhi math. nauk, 54:2 (1999), 165–166 | DOI | MR | Zbl

[5] I.Kh. Sabitov, “Algebraic methodes for solution of polyhedra”, Uspekhi math. nauk, 66:3 (2011), 3–66 | DOI | MR | Zbl

[6] D.I. Sabitov, I.Kh. Sabitov, “Volume polynomials for polyhedra of hexagonal type”, Siberian Electronic Mathematical Reports, 14 (2017), 1078–1087 | MR | Zbl

[7] A.V. Astrelin, I.Kh. Sabitov, “A minimal-degree polynomial for detemining the volume of an octahedron from its metrice”, Uspekhi math. nauk, 50:5 (1995), 245–246 | MR | Zbl

[8] D.I. Sabitov, I.Kh. Sabitov, “Volume polynomials for some polyhedra in spaces of constant curvature”, Modelirovanie i analys informatsionnykh system, 19:6 (2012), 159–167

[9] N.P. Dolbilin, M.A. Shtan'ko, M.I. Shtogrin, “On rigidity of polyhedral spheres with even-angle faces”, Uspekhi math. nauk, 51:3 (1996), 197–198 | DOI | MR | Zbl

[10] N.P. Dolbilin, M.A. Shtan'ko, M.I. Shtogrin, “Rigidity of a quadrillage of the torus”, Uspekhi math. nauk, 54:4 (1999), 167–168 | DOI | MR | Zbl

[11] M.I. Shtogrin, “Rigidity of a quadrillage of the pretzel”, Uspekhi math. nauk, 54:5 (1999), 183–184 | DOI | MR | Zbl

[12] V.A. Alexandrov, “A new example of a flexing polyhedron”, Sibirskii matem. jurnal, 36:6 (1995), 1215–1224 | MR

[13] M.I. Shtogrin, “On flexible polyhedral surfaces”, Trudy MIAN imeni Steklova, 288, 2015, 171–183 | MR | Zbl