A New Bound for Hadwiger’s Covering Problem in \(\boldsymbol{\mathbb{E}}^3\)

Abstract

We show that every three-dimensional convex body can be covered by 14 smaller homothetic copies. The previous result was 16 established by Papadoperakis in 1999, while a conjecture by Hadwiger is 8. We develop a discretization technique showing that it suffices to verify the feasibility of a number of linear programs with rational coefficients, which is done with computer assistance using exact arithmetic.