
This article is cited in 1 scientific paper (total in 1 paper)
Volume Polynomials for Some Polyhedra in Spaces of Constant Curvature
D. I. Sabitov^{a}, I. Kh. Sabitov^{ab} ^{a} M. V. Lomonosov Moscow State University
^{b} P. G. Demidov Yaroslavl State University
Abstract:
It is known that for each simplicial polyhedron $P$ in 3space 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.
Keywords:
polyhedra, metrics, pyramids, volumes, polynomials.
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UDC:
514.772.35 Received: 15.09.2012
Citation:
D. I. Sabitov, I. Kh. Sabitov, “Volume Polynomials for Some Polyhedra in Spaces of Constant Curvature”, Model. Anal. Inform. Sist., 19:6 (2012), 161–169
Citation in format AMSBIB
\Bibitem{SabSab12}
\by D.~I.~Sabitov, I.~Kh.~Sabitov
\paper Volume Polynomials for Some Polyhedra in Spaces of Constant Curvature
\jour Model. Anal. Inform. Sist.
\yr 2012
\vol 19
\issue 6
\pages 161169
\mathnet{http://mi.mathnet.ru/mais281}
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http://mi.mathnet.ru/eng/mais281 http://mi.mathnet.ru/eng/mais/v19/i6/p161
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L. N. Romakina, “On the area of a trihedral on a hyperbolic plane of positive curvature”, Siberian Adv. Math., 25:2 (2015), 138–153

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