  We show an explicit construction in 3 dimensions for a convex,
mono-monostatic polyhedron (i.e., having exactly one stable and one unstable
equilibrium) with 21 vertices and 21 faces. This polyhedron is a 0-skeleton,
with equal masses located at each vertex. The above construction serves as an
upper bound for the minimal number of faces and vertices of mono-monostatic
0-skeletons and complements the recently provided lower bound of 8 vertices.
This is the first known construction of a mono-monostatic polyhedral solid. We
also show that a similar construction for homogeneous distribution of mass
cannot result in a mono-monostatic solid.
