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.

Location: http://mech.math.msu.su/~fpm/eng/k08/k082/k08209h.htm

Last modified: December 18, 2008