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JOURNALS // Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya // Archive

Izv. RAN. Ser. Mat., 2002 Volume 66, Issue 2, Pages 159–172 (Mi im382)

This article is cited in 9 papers

Algorithmic solution of the problem of isometric realization for two-dimensional polyhedral metrics

I. Kh. Sabitov

M. V. Lomonosov Moscow State University

Abstract: For polyhedra in general position that have a given combinatorial structure, an algorithm is suggested for finding all their metric characteristics, namely, their volumes, dihedral angles, and diagonals, from the lengths of their edges, and thus the possibility of developing a new line of geometric investigation is established, which, in analogy with the well-known term “solution of a triangle”, can be called “solution of a polyhedron”.

UDC: 513.7

MSC: 51M25, 52C25, 52B11, 57R42, 68U05, 68W30

Received: 12.12.2000

DOI: 10.4213/im382


 English version:
Izvestiya: Mathematics, 2002, 66:2, 377–391

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