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Matematicheskie Trudy, 2008, Volume 11, Number 1, Pages 132–152 (Mi mt120)  

This article is cited in 4 scientific papers (total in 4 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
Full-text PDF (641 kB) Citations (4)
References:
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.
Received: 28.10.2007
English version:
Siberian Advances in Mathematics, 2009, Volume 19, Issue 4, Pages 287–300
DOI: https://doi.org/10.3103/S1055134409040063
Bibliographic databases:
UDC: 514.12+512.542.2
Language: Russian
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://mathscinet.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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  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические труды Siberian Advances in Mathematics
     
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