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arXiv · 2112.10698

Every $3$-dimensional convex body can be covered by $14$ smaller homothetic copies

A. Prymak
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Abstract

We show that every $3$-dimensional convex body can be covered by $14$ smaller homothetic copies. The previous result was $16$ copies established by Papadoperakis in 1999, while a conjecture by Hadwiger is $8$. We modify Papadoperakis's approach and develop a discretization technique that reduces the problem to verification of feasibility of a number of linear programs with rational coefficients, which is done with computer assistance using exact arithmetic.

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A. Prymak. 2021-12-20. Every $3$-dimensional convex body can be covered by $14$ smaller homothetic copies. https://doi.org/10.1137/22m1490314

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