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
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.
convex polyhedra, group of isometries, regular faces, computer algebra.
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Siberian Advances in Mathematics, 2009, 19:4, 287–300
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
\paper Convex regular-faced polyhedra indecomposable by any plane to regular-faced polyhedra
\jour Mat. Tr.
\jour Siberian Adv. Math.
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This publication is cited in the following articles:
A. V. Timofeenko, “Junction of noncomposite polygons”, St. Petersburg Math. J., 21:3 (2010), 483–512
Timofeenko A.V., “Convex polyhedra with parquet faces”, Dokl. Math., 80:2 (2009), 720–723
A. V. Timofeenko, “O vypuklykh mnogogrannikakh s ravnougolnymi i parketnymi granyami”, Chebyshevskii sb., 12:2 (2011), 118–126
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