Relationships between Widths of a Convex Body and of an Inscribed Parallelotope

Marek Lassak
Institut für Informatik
Freie Universität Berlin
Takustr. 9, D-14195 Berlin
email: lassak@inf.fu-berlin.de

Report B 00-08
April 2000

Abstract
Assume that a parallelotope P is inscribed in a three-dimensional convex body C. A conjecture says that w^-1₁+w^-1₂+w^-1₃>=1, where w_i is the ratio of the width of C to the width of P for the direction perpendicular to the i-th pair of parallel facets of P. We prove three weaker inequalities. One of them is w^-1₁+w^-1₂+a^-1₃>=1, where a₃ denotes the related axial diameter of C.

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