Stable and Unstable Faces of Antiprisms
A face of a polyhedron is stable if and only if the orthogonal projection of the center of mass onto the face lies inside the face or on one of its edges. This Demonstration shows that antiprisms with sufficiently small heights are stable only on their bases.
Reference  J. Bryant and C. Sangwin, How Round Is Your Circle?: Where Engineering and Mathematics Meet, Princeton, NJ: Princeton University Press, 2008, pp. 273–274.