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Izvestiya: Mathematics, 2005, Volume 69, Issue 4, Pages 847–864
DOI: https://doi.org/10.1070/IM2005v069n04ABEH001667 (Mi im653) 		 
This article is cited in 2 scientific papers (total in 2 papers)

On the structure of faces of three-dimensional polytopes

M. I. Shtogrin

Steklov Mathematical Institute, Russian Academy of Sciences
English version PDF (267 kB) Citations (2)
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DOI: https://doi.org/10.1070/IM2005v069n04ABEH001667
Abstract: In Euclidean three-space, we consider two-dimensional polyhedra that are homeomorphic to closed surfaces. The structure of an arbitrary face of such a polyhedron is studied in detail. In particular, we prove the following main theorem. If a two-dimensional polyhedron lies in Euclidean three-space and is isometric to the surface of a convex three-dimensional polytope, then all the faces of the polyhedron are convex polygons.
Received: 19.01.2005
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2005, Volume 69, Issue 4, Pages 205–224
DOI: https://doi.org/10.4213/im653
Bibliographic databases:
Document Type: Article
UDC: 514.113.5+514.172.45
MSC: 52B10, 52C25, 53C45
Language: English
Original paper language: Russian
Citation: M. I. Shtogrin, “On the structure of faces of three-dimensional polytopes”, Izv. RAN. Ser. Mat., 69:4 (2005), 205–224; Izv. Math., 69:4 (2005), 847–864
Citation in format AMSBIB
\Bibitem{Sht05}
\by M.~I.~Shtogrin
\paper On~the structure of~faces of~three-dimensional polytopes
\jour Izv. RAN. Ser. Mat.
\yr 2005
\vol 69
\issue 4
\pages 205--224
\mathnet{http://mi.mathnet.ru/im653}
\crossref{https://doi.org/10.4213/im653}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2170708}
\zmath{https://zbmath.org/?q=an:1085.52006}
\elib{https://elibrary.ru/item.asp?id=9195229}
\transl
\jour Izv. Math.
\yr 2005
\vol 69
\issue 4
\pages 847--864
\crossref{https://doi.org/10.1070/IM2005v069n04ABEH001667}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33645516361}
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  • https://doi.org/10.1070/IM2005v069n04ABEH001667
  • https://www.mathnet.ru/eng/im/v69/i4/p205
    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:474
    Russian version PDF:273
    English version PDF:9
    References:56
    First page:3
     
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