%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 }