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Fundam. Prikl. Mat., 2008, Volume 14, Issue 2, Pages 179–205 (Mi fpm1119)  

This article is cited in 3 scientific papers (total in 4 papers)

The non-Platonic and non-Archimedean noncomposite polyhedra

A. V. Timofeenko

Krasnoyarsk State Pedagogical University named after V. P. Astaf'ev

Abstract: If a convex polyhedron with regular faces cannot be divided by any plane into two polyhedra with regular faces, then it is said to be noncomposite. We indicate the exact coordinates of the vertices of noncomposite polyhedra that are neither regular (Platonic), nor semiregular (Archimedean), nor their parts cut by no more than three planes. Such a description allows one to obtain a short proof of the existence of each of the eight such polyhedra (denoted by $M_8$, $M_{20}$$M_{25}$, $M_{28}$) and to obtain other applications.

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English version:
Journal of Mathematical Sciences (New York), 2009, 162:5, 710–729

Bibliographic databases:

UDC: 514.12+512.542.2
Received: 01.01.2005

Citation: A. V. Timofeenko, “The non-Platonic and non-Archimedean noncomposite polyhedra”, Fundam. Prikl. Mat., 14:2 (2008), 179–205; J. Math. Sci., 162:5 (2009), 710–729

Citation in format AMSBIB
\Bibitem{Tim08}
\by A.~V.~Timofeenko
\paper The non-Platonic and non-Archimedean noncomposite polyhedra
\jour Fundam. Prikl. Mat.
\yr 2008
\vol 14
\issue 2
\pages 179--205
\mathnet{http://mi.mathnet.ru/fpm1119}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2475600}
\zmath{https://zbmath.org/?q=an:1185.52011}
\elib{http://elibrary.ru/item.asp?id=12197924}
\transl
\jour J. Math. Sci.
\yr 2009
\vol 162
\issue 5
\pages 710--729
\crossref{https://doi.org/10.1007/s10958-009-9655-0}
\elib{http://elibrary.ru/item.asp?id=15301434}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-70350676300}


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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, “Convex regular-faced polyhedra indecomposable by any plane to regular-faced polyhedra”, Siberian Adv. Math., 19:4 (2009), 287–300  mathnet  crossref  mathscinet
    2. A. V. Timofeenko, “Junction of noncomposite polygons”, St. Petersburg Math. J., 21:3 (2010), 483–512  mathnet  crossref  mathscinet  zmath  isi
    3. A. M. Gurin, “K istorii izucheniya vypuklykh mnogogrannikov s pravilnymi granyami”, Sib. elektron. matem. izv., 7 (2010), 5–23  mathnet
    4. A. V. Timofeenko, “O vypuklykh mnogogrannikakh s ravnougolnymi i parketnymi granyami”, Chebyshevskii sb., 12:2 (2011), 118–126  mathnet  mathscinet
  • Фундаментальная и прикладная математика
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