Decomposing the 2-sphere into domains of smallest possible diameter (Q1307426)

A classic problem in discrete geometry is to find, for a given natural number \(n\), the smallest \(\delta\) such that the sphere can be covered by \(n\) circular regions of diameter \(\leq \delta\). The paper under review concerns a related sphere decomposition problem in which the shape of the covering sets is relaxed: to find the smallest value \(\sigma (n)\) such that the sphere can be decomposed to \(n\) sets each of (spherical) diameter \(\leq \sigma (n)\). The value of \(\sigma (n)\) is determined precisely for \(n < 7\) and \(n = 8,9\). Upper bounds on \(\sigma (n)\) are given for \(n = 7, 10, 12\).