Shape from silhouettes is a binary geometric tomography since both objects and projections, which are measured as silhouettes, are binary. In this paper, we formulate shape from silhouettes in the three-dimensional discrete space. This treatment of the problem implies an ambiguity theorem for the reconstruction of objects in discrete space. Furthermore, we show that in three-dimensional space, it is possible to reconstruct a class of non-convex objects from a collection of silhouettes though on a plane non-convex object is unreconstractable from any collection of silhouettes.