D97: Search for small monostatic polyhedra


We study a class of convex polyhedra that contains the famous 19-face monostatic polyhedron discovered by R. K. Guy in 1969. The properties of the polyhedra of this class allow to efficiently scan them so that it becomes possible to check in a reasonable time, with a computer program, whether the class contains a convex monostatic polyhedron with fewer than 19 faces.