  This article is concerned with the problem of approximating a not necessarily
bounded spectrahedral shadow, a certain convex set, by polyhedra. By
identifying the set with its homogenization the problem is reduced to the
approximation of a closed convex cone. We introduce the notion of homogeneous
{\delta}-approximation of a convex set and show that it defines a meaningful
concept in the sense that approximations converge to the original set if the
approximation error {\delta} diminishes. Moreover, we show that a homogeneous
{\delta}-approximation of the polar of a convex set is immediately available
from an approximation of the set itself under mild conditions. Finally, we
present an algorithm for the computation of homogeneous {\delta}-approximations
of spectrahedral shadows and demonstrate it on examples.
