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Izv. RAN. Ser. Mat., 2002, Volume 66, Issue 2, Pages 159–172 (Mi izv382)  

This article is cited in 7 scientific papers (total in 7 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”.

DOI: https://doi.org/10.4213/im382

Full text: PDF file (1429 kB)
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English version:
Izvestiya: Mathematics, 2002, 66:2, 377–391

Bibliographic databases:

UDC: 513.7
MSC: 51M25, 52C25, 52B11, 57R42, 68U05, 68W30
Received: 12.12.2000

Citation: I. Kh. Sabitov, “Algorithmic solution of the problem of isometric realization for two-dimensional polyhedral metrics”, Izv. RAN. Ser. Mat., 66:2 (2002), 159–172; Izv. Math., 66:2 (2002), 377–391

Citation in format AMSBIB
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  • https://doi.org/10.4213/im382
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. N. Mikhalev, “Izometricheskie realizatsii oktaedrov Brikara 1-go i 2-go tipa s izvestnymi znacheniyami ob'ema”, Fundament. i prikl. matem., 8:3 (2002), 755–768  mathnet  mathscinet  zmath
    2. Sabitov I., “Solution of polyhedra”, Bull. Braz. Math. Soc. (N.S.), 35:2 (2004), 199–210  crossref  mathscinet  zmath  isi  elib  scopus
    3. Fedorchuk M., Pak I., “Rigidity and polynomial invariants of convex polytopes”, Duke Math. J., 129:2 (2005), 371–404  crossref  mathscinet  zmath  isi  elib  scopus
    4. S. N. Mikhalev, “A method for solving the problem of isometric realization of developments”, J. Math. Sci., 149:1 (2008), 971–995  mathnet  crossref  mathscinet  zmath  elib
    5. I. Kh. Sabitov, “Algebraic methods for solution of polyhedra”, Russian Math. Surveys, 66:3 (2011), 445–505  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    6. I. Kh. Sabitov, “On a class of inflexible polyhedra”, Siberian Math. J., 55:5 (2014), 961–967  mathnet  crossref  mathscinet  isi
    7. I. Kh. Sabitov, “The Moscow Mathematical Society and metric geometry: from Peterson to contemporary research”, Trans. Moscow Math. Soc., 77 (2016), 149–175  mathnet  crossref  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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