Volume Polynomials for Some Polyhedra in Spaces of Constant Curvature
It is known that for each simplicial polyhedron P in 3-space there exists a monic polynomial Q depending on the combinatorial structure of P and the lengths of its edges only such that the volume of the polyhedron P as well as one of any polyhedron isometric to P and with the same combinatorial stru...
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Yaroslavl State University
2015-03-01
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| Series: | Моделирование и анализ информационных систем |
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| Online Access: | https://www.mais-journal.ru/jour/article/view/151 |
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| author | D. I. Sabitov I. Kh. Sabitov |
| author_facet | D. I. Sabitov I. Kh. Sabitov |
| author_sort | D. I. Sabitov |
| collection | DOAJ |
| description | It is known that for each simplicial polyhedron P in 3-space there exists a monic polynomial Q depending on the combinatorial structure of P and the lengths of its edges only such that the volume of the polyhedron P as well as one of any polyhedron isometric to P and with the same combinatorial structure are roots of the polynomial Q. But this polynomial contains many millions of terms and it cannot be presented in an explicit form. In this work we indicate some special classes of polyhedra for which these polynomials can be found by a sufficiently effective algorithm which also works in spaces of constsnt curvature of any dimension. |
| format | Article |
| id | doaj-art-5b51c7e0e069469f97c9b2f64e2799e0 |
| institution | Matheson Library |
| issn | 1818-1015 2313-5417 |
| language | English |
| publishDate | 2015-03-01 |
| publisher | Yaroslavl State University |
| record_format | Article |
| series | Моделирование и анализ информационных систем |
| spelling | doaj-art-5b51c7e0e069469f97c9b2f64e2799e02025-08-04T14:06:41ZengYaroslavl State UniversityМоделирование и анализ информационных систем1818-10152313-54172015-03-0119616116910.18255/1818-1015-2012-6-161-169145Volume Polynomials for Some Polyhedra in Spaces of Constant CurvatureD. I. Sabitov0I. Kh. Sabitov1Московский государственный университет им. М.В. ЛомоносоваМосковский государственный университет им. М.В. Ломоносова; Ярославский государственный университет им. П.Г. Демидова, Международная лаборатория "Дискретная и вычислительная геометрия" им. Б.Н. ДелонеIt is known that for each simplicial polyhedron P in 3-space there exists a monic polynomial Q depending on the combinatorial structure of P and the lengths of its edges only such that the volume of the polyhedron P as well as one of any polyhedron isometric to P and with the same combinatorial structure are roots of the polynomial Q. But this polynomial contains many millions of terms and it cannot be presented in an explicit form. In this work we indicate some special classes of polyhedra for which these polynomials can be found by a sufficiently effective algorithm which also works in spaces of constsnt curvature of any dimension.https://www.mais-journal.ru/jour/article/view/151polyhedrametricspyramidsvolumespolynomials |
| spellingShingle | D. I. Sabitov I. Kh. Sabitov Volume Polynomials for Some Polyhedra in Spaces of Constant Curvature Моделирование и анализ информационных систем polyhedra metrics pyramids volumes polynomials |
| title | Volume Polynomials for Some Polyhedra in Spaces of Constant Curvature |
| title_full | Volume Polynomials for Some Polyhedra in Spaces of Constant Curvature |
| title_fullStr | Volume Polynomials for Some Polyhedra in Spaces of Constant Curvature |
| title_full_unstemmed | Volume Polynomials for Some Polyhedra in Spaces of Constant Curvature |
| title_short | Volume Polynomials for Some Polyhedra in Spaces of Constant Curvature |
| title_sort | volume polynomials for some polyhedra in spaces of constant curvature |
| topic | polyhedra metrics pyramids volumes polynomials |
| url | https://www.mais-journal.ru/jour/article/view/151 |
| work_keys_str_mv | AT disabitov volumepolynomialsforsomepolyhedrainspacesofconstantcurvature AT ikhsabitov volumepolynomialsforsomepolyhedrainspacesofconstantcurvature |