Geodesic
Algebraic methods for solution of polyhedra
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 66 (2011) no. 3, pp. 445-505

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

By analogy with the solution of triangles, the solution of polyhedra means a theory and methods for calculating some geometric parameters of polyhedra in terms of other parameters of them. The main content of this paper is a survey of results on calculating the volumes of polyhedra in terms of their metrics and combinatorial structures. It turns out that a far-reaching generalization of Heron's formula for the area of a triangle to the volumes of polyhedra is possible, and it underlies the proof of the conjecture that the volume of a deformed flexible polyhedron remains constant. Bibliography: 110 titles.
Keywords: polyhedra, combinatorial structure, metric, bending, bellows conjecture, volume polynomials, generalization of Heron's formula.
Mots-clés : volume 
@article{RM_2011_66_3_a0,
     author = {I. Kh. Sabitov},
     title = {Algebraic methods for solution of polyhedra},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {445--505},
     publisher = {mathdoc},
     volume = {66},
     number = {3},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RM_2011_66_3_a0/}
}
TY  - JOUR
AU  - I. Kh. Sabitov
TI  - Algebraic methods for solution of polyhedra
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2011
SP  - 445
EP  - 505
VL  - 66
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/RM_2011_66_3_a0/
LA  - en
ID  - RM_2011_66_3_a0
ER  - 
%0 Journal Article
%A I. Kh. Sabitov
%T Algebraic methods for solution of polyhedra
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2011
%P 445-505
%V 66
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/RM_2011_66_3_a0/
%G en
%F RM_2011_66_3_a0
I. Kh. Sabitov. Algebraic methods for solution of polyhedra. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 66 (2011) no. 3, pp. 445-505. http://geodesic.mathdoc.fr/item/RM_2011_66_3_a0/