Before revision:  We are given a convex body K of unit diameter in Euclidean d-dimensional space (where d is a constant) along with an error parameter \varepsilon > 0. The objective is to determine a  polytope of low combinatorial complexity whose Hausdorff distance from K is at most \varepsilon.
After revision:  We are given a convex body K of unit diameter in Euclidean d-dimensional space (where d is a constant) along with an error parameter \varepsilon > 0, the objective is to determine a polytope of low combinatorial complexity whose Hausdorff distance from K is at most \varepsilon.