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Mat. Tr., 2008, Volume 11, Number 1, Pages 132–152 (Mi mt120)  

This article is cited in 3 scientific papers (total in 3 papers)

Convex regular-faced polyhedra indecomposable by any plane to regular-faced polyhedra

A. V. Timofeenko

Institute of Computational Modelling, Siberian Branch of the Russian Academy of Sciences

Abstract: A convex polyhedron with regular faces or with faces decomposable by two regular polygons is called indecomposable if any section plane dissects this polyhedron by such two parts that at least one of the faces of these two parts is an irregular polygon. In this article, the precise values of coordinates of vertices of such indecomposable convex polyhedra are calculated in the case when some of the faces consist of two regular polygons. The algebraic models of other indecomposable polyhedra have constructed. So, for any indecomposable convex polyhedron, we give here the explicit values of coordinates of such vertices and describe isometries of the space such that the collection of orbits of these vertices under action of the group generated by these isometries coincides with the set of all vertices of this polyhedron.
This description provides a short proof of existence of each of these indecomposable polyhedra, and some other applications as well.

Key words: convex polyhedra, group of isometries, regular faces, computer algebra.

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English version:
Siberian Advances in Mathematics, 2009, 19:4, 287–300

Bibliographic databases:

UDC: 514.12+512.542.2
Received: 28.10.2007

Citation: A. V. Timofeenko, “Convex regular-faced polyhedra indecomposable by any plane to regular-faced polyhedra”, Mat. Tr., 11:1 (2008), 132–152; Siberian Adv. Math., 19:4 (2009), 287–300

Citation in format AMSBIB
\Bibitem{Tim08}
\by A.~V.~Timofeenko
\paper Convex regular-faced polyhedra indecomposable by any plane to regular-faced polyhedra
\jour Mat. Tr.
\yr 2008
\vol 11
\issue 1
\pages 132--152
\mathnet{http://mi.mathnet.ru/mt120}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2437485}
\transl
\jour Siberian Adv. Math.
\yr 2009
\vol 19
\issue 4
\pages 287--300
\crossref{https://doi.org/10.3103/S1055134409040063}


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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. A. V. Timofeenko, “Junction of noncomposite polygons”, St. Petersburg Math. J., 21:3 (2010), 483–512  mathnet  crossref  mathscinet  zmath  isi
    2. Timofeenko A.V., “Convex polyhedra with parquet faces”, Dokl. Math., 80:2 (2009), 720–723  mathnet  crossref  mathscinet  zmath  isi  elib  elib  scopus
    3. A. V. Timofeenko, “O vypuklykh mnogogrannikakh s ravnougolnymi i parketnymi granyami”, Chebyshevskii sb., 12:2 (2011), 118–126  mathnet  mathscinet
  • Математические труды Siberian Advances in Mathematics
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