  We introduce the vertex index, vein(K), of a given centrally symmetric convex
body K, which, in a sense, measures how well K can be inscribed into a convex
polytope with small number of vertices. This index is closely connected to the
illumination parameter of a body, introduced earlier by the first named author,
and, thus, related to the famous conjecture in Convex Geometry about covering
of a d-dimensional body by 2^d smaller positively homothetic copies. We provide
asymptotically sharp estimates (up to a logarithmic term) of this index in the
general case. Also, we provide sharp estimates in dimensions 2 and 3.
