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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2019, Volume 305, Pages 86–147
DOI: https://doi.org/10.4213/tm4010
(Mi tm4010)
 

This article is cited in 4 scientific papers (total in 4 papers)

Three-Dimensional Right-Angled Polytopes of Finite Volume in the Lobachevsky Space: Combinatorics and Constructions

N. Yu. Erokhovets

Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119991 Russia
Full-text PDF (775 kB) Citations (4)
References:
Abstract: We study combinatorial properties of polytopes realizable in the Lobachevsky space $\mathbb L^3$ as polytopes of finite volume with right dihedral angles. On the basis of E. M. Andreev's theorem we prove that cutting off ideal vertices of right-angled polytopes defines a one-to-one correspondence with strongly cyclically four-edge-connected polytopes different from the cube and the pentagonal prism. We show that any polytope of the latter family can be obtained by cutting off a matching of a polytope from the same family or of the cube with at most two nonadjacent orthogonal edges cut, in such a way that each quadrangle results from cutting off an edge. We refine D. Barnette's construction of this family of polytopes and present its application to right-angled polytopes. We refine the known construction of ideal right-angled polytopes using edge twists and describe its connection with D. Barnette's construction via perfect matchings. We make a conjecture on the behavior of the volume under operations and give arguments to support it.
Funding agency Grant number
Russian Foundation for Basic Research 17-01-00671
16-51-55017
The work was supported by the Russian Foundation for Basic Research, project nos. 17-01-00671 and 16-51-55017-GFEN.
Received: December 30, 2018
Revised: March 11, 2019
Accepted: March 13, 2019
English version:
Proceedings of the Steklov Institute of Mathematics, 2019, Volume 305, Pages 78–134
DOI: https://doi.org/10.1134/S0081543819030064
Bibliographic databases:
Document Type: Article
UDC: 514.172.45+514.132+519.17
Language: Russian
Citation: N. Yu. Erokhovets, “Three-Dimensional Right-Angled Polytopes of Finite Volume in the Lobachevsky Space: Combinatorics and Constructions”, Algebraic topology, combinatorics, and mathematical physics, Collected papers. Dedicated to Victor Matveevich Buchstaber, Corresponding Member of the Russian Academy of Sciences, on the occasion of his 75th birthday, Trudy Mat. Inst. Steklova, 305, Steklov Math. Inst. RAS, Moscow, 2019, 86–147; Proc. Steklov Inst. Math., 305 (2019), 78–134
Citation in format AMSBIB
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\paper Three-Dimensional Right-Angled Polytopes of Finite Volume in the Lobachevsky Space: Combinatorics and Constructions
\inbook Algebraic topology, combinatorics, and mathematical physics
\bookinfo Collected papers. Dedicated to Victor Matveevich Buchstaber, Corresponding Member of the Russian Academy of Sciences, on the occasion of his 75th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2019
\vol 305
\pages 86--147
\publ Steklov Math. Inst. RAS
\publaddr Moscow
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  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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