FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2008, VOLUME 14, NUMBER 2, PAGES 179-205

The non-Platonic and non-Archimedean noncomposite polyhedra

A. V. Timofeenko

Abstract

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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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Last modified: December 18, 2008