2021/03/18 by Lian, Yanlu, zhang, Yuqin
#52A15 #52C07 #52C17 #FOS: Mathematics #Metric Geometry (math.MG)
paper · doi:10.48550/arxiv.2103.10004
In 1957, Hadwiger made the famous conjecture that any convex body of n-dimensional Euclidean space 𝔼n can be covered by 2n smaller positive homothetic copies. Up to now, this conjecture is still open for all n≥ 3. Denote by γm(K) the smallest positive number λ such that K can be covered by m translations of λK. The values of γm(K) for some particular m and K have been studied. In this article, we will focus on the situation where K is the unit crosspolytope of the three-dimensional.