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The non-platonic and non-Archimedean noncomposite polyhedra

  • A. V. Timofeenko
Article
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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 20M 25, M 28) and to obtain other applications.

Keywords

Computer Algebra System Convex Polyhedron Common Edge Identical Transformation Triangular Face 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media, Inc. 2009

Authors and Affiliations

  1. 1.Krasnoyarsk State Pedagogical UniversityKrasnoyarskRussia

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