This note discusses the derivation of a polynomial for the volume
of a octahedron, when the edge lengths of it are given. It is known
that the volume of a flexible polyhedron with those edge lengths
doesn't depend on the realization. For octahedra there are 8 realizations,
and therefore the polynomial that describes the volume must have
degree 8. The derivation of this polynomial is done by using a computer
algebra system.
%0 Journal Article
%1 863.68076
%A Astrelin, A.V.
%A Sabitov, I.Kh.
%D 1995
%J Russ. Math. Surv.
%K a algebra} computer derivation octahedron; of polyhedra; polynomial; volume; {flexible
%N 5
%P 1085-1087
%T A minimal-degree polynomial for determining the volume of an octahedron
from its metric.
%V 50
%X This note discusses the derivation of a polynomial for the volume
of a octahedron, when the edge lengths of it are given. It is known
that the volume of a flexible polyhedron with those edge lengths
doesn't depend on the realization. For octahedra there are 8 realizations,
and therefore the polynomial that describes the volume must have
degree 8. The derivation of this polynomial is done by using a computer
algebra system.
@article{863.68076,
abstract = {{This note discusses the derivation of a polynomial for the volume
of a octahedron, when the edge lengths of it are given. It is known
that the volume of a flexible polyhedron with those edge lengths
doesn't depend on the realization. For octahedra there are 8 realizations,
and therefore the polynomial that describes the volume must have
degree 8. The derivation of this polynomial is done by using a computer
algebra system.} },
added-at = {2008-03-02T02:12:02.000+0100},
author = {Astrelin, A.V. and Sabitov, I.Kh.},
biburl = {https://www.bibsonomy.org/bibtex/24cfb3db1b445c824723b35c0a7c49ec6/dmartins},
classmath = {{*68Q40 Symbolic computation, algebraic computation 68U05 Computational
geometry, etc.}},
description = {robotica-bib},
interhash = {61c09714757e53238ae558a6d978d2c6},
intrahash = {4cfb3db1b445c824723b35c0a7c49ec6},
journal = {Russ. Math. Surv.},
keywords = {a algebra} computer derivation octahedron; of polyhedra; polynomial; volume; {flexible},
language = {English. Russian original},
number = 5,
pages = {1085-1087},
reviewer = {{M.van Kreveld (Utrecht)}},
timestamp = {2008-03-02T02:12:13.000+0100},
title = {{A minimal-degree polynomial for determining the volume of an octahedron
from its metric.} },
volume = 50,
year = 1995
}