**Beiträge zur Algebra und Geometrie
**

Contributions to Algebra and Geometry

Vol. 39, No. 2, pp. 259-262 (1998)

#
Covering a Three-Dimensional Convex Body by Smaller Homothetic Copies

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M. Lassak

Instytut Matematyki i Fizyki ATR, ul. Kaliskiego 7, 85-796 Bydgoszcz, Poland, e-mail: lassak@atr.bydgoszcz.pl

**Abstract:** We show that every three-dimensional convex body $C$ can be covered by $20$ smaller positive homothetic copies. The homothety ratio here depends on $C$. Under the requirement that the homothety ratio is universal, such a covering is possible by $24$ copies.

**Classification (MSC91):** 52C17

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