FINITE AND UNIFORM STABILITY OF SPHERE COVERINGS

By attaching cables to the centers of the balls and certain intersecti ons of the boundaries of the balls of a ball covering of E(d) With uni t balls, we can associate to any ball covering a collection of cabled frameworks. It turns out that a finite subset of balls can be moved, m aintaining the covering property, if and only if the corresponding fin ite subframework in one of the cabled frameworks is not rigid. As an a pplication of this cabling technique we show that the thinnest cubic l attice sphere covering of E(d) is not finitely stable.