Inscribed and Circumscribed Polyhedra for a Centrally Symmetric Convex Body

V. V. Makeev, N. Yu. Netsvetaev

Research output

Abstract

We construct new polyhedra such that some of their similar or affine images can be inscribed in (or circumscribed about) every centrally symmetric convex body.

One of the main theorems is as follows. If K is a centrally symmetric, three-dimensional, convex body, then either an affine-regular dodecahedron is inscribed in K or there are two affine-regular dodecahedra D1 and D2 such that nine pairs of opposite vertices of Di, i = 1, 2, lie on the boundary of K. Furthermore, the remaining two vertices of D1 lie outside K, while the remaining two vertices of D2 lie inside K.
Original languageEnglish
Pages (from-to)552-557
Number of pages6
JournalJournal of Mathematical Sciences
Volume212
Issue number5
Early online date8 Jan 2016
Publication statusPublished - 2016

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