Before revision: Let P be a set of n points in \Re^d in general position. A median hyperplane (roughly) splits the point set P in half. The yolk of P is the ball of smallest radius intersecting all median hyperplanes of P. The egg of P is the ball of smallest radius intersecting all hyperplanes which contain exactly d points of P. We present exact \Re{R}  algorithms for computing the yolk and the egg of a point set, both running in expected time O(n ^{d-1 \log n) .
After revision:  \Re{R} algorithms for computing the yolk and the egg of a point set, both running in expected time O(n ^{d-1 \log n) .