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Chebyshevskii Sb., 2020, Volume 21, Issue 2, Pages 65–83 (Mi cheb896)  

Ideal right-angled polyhedra in Lobachevsky space

A. Yu. Vesninabc, A. A. Egorovba

a Tomsk State University, Tomsk
b Novosibirsk State University, Novosibirsk
c Sobolev Institute of Mathematics, Novosibirsk

Abstract: In this paper we consider a class of right-angled polyhedra in three-dimensional Lobachevsky space, all vertices of which lie on the absolute. New upper bounds on volumes in terms the number of faces of the polyhedron are obtained. Volumes of polyhedra with at most 23 faces are computed. It is shown that the minimum volumes are realized on antiprisms and twisted antiprisms. The first 248 values of volumes of ideal right-angled polyhedra are presented. Moreover, the class of polyhedra with isolated triangles is introduces and there are obtained combinatorial bounds on their existence as well as minimal examples of such polyhedra are given.

Keywords: Hyperbolic 3-space, ideal polyhedron, right-angled polyhedron, antiprism.

Funding Agency Grant Number
Russian Foundation for Basic Research 19-01-00569


DOI: https://doi.org/10.22405/2226-8383-2018-21-2-65-83

Full text: PDF file (2106 kB)
References: PDF file   HTML file

UDC: 515.162.8 + 514.132
Received: 14.12.2019
Accepted:11.03.2020
Language:

Citation: A. Yu. Vesnin, A. A. Egorov, “Ideal right-angled polyhedra in Lobachevsky space”, Chebyshevskii Sb., 21:2 (2020), 65–83

Citation in format AMSBIB
\Bibitem{VesEgo20}
\by A.~Yu.~Vesnin, A.~A.~Egorov
\paper Ideal right-angled polyhedra in Lobachevsky space
\jour Chebyshevskii Sb.
\yr 2020
\vol 21
\issue 2
\pages 65--83
\mathnet{http://mi.mathnet.ru/cheb896}
\crossref{https://doi.org/10.22405/2226-8383-2018-21-2-65-83}


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