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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
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.
Received: December 30, 2018 Revised: March 11, 2019 Accepted: March 13, 2019
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
Linking options:
https://www.mathnet.ru/eng/tm4010https://doi.org/10.4213/tm4010 https://www.mathnet.ru/eng/tm/v305/p86
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Abstract page: | 474 | Full-text PDF : | 162 | References: | 38 | First page: | 15 |
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