The smallest mono-unstable, homogeneous convex polyhedron has at least 7 vertices

Sándor Bozóki, Gábor Domokos, Dávid Papp +1

We prove that every homogeneous convex polyhedron with only one unstable equilibrium (known as a mono-unstable convex polyhedron) has at least $7$ vertices. Although it has been lo…