  We propose a randomized algorithm for enumerating the vertices of a zonotope,
which is a low-dimensional linear projection of a hypercube. The algorithm
produces a pair of the zonotope's vertices by sampling a random linear
combination of the zonotope generators, where the combination's weights are the
signs of the product between the zonotope's generator matrix and random vectors
with normally distributed entries. We study the probability of recovering
particular vertices and relate it to the vertices' normal cones. This study
shows that if we terminate the randomized algorithm before all vertices are
recovered, then the convex hull of the resulting vertex set approximates the
zonotope. In high dimensions, we expect the enumeration algorithm to be most
appropriate as an approximation algorithm---particularly for cases when
existing methods are not practical.
