Szilassi polyhedron
The Szilassi polyhedron has seven hexagonal faces. Topologically it is a torus, that is, if it were smoothed out, it might be a "doughnut".
It was discovered in 1977 by Hungarian mathematician Lajos Szilassi with support of computer based calculations. This GeoGebra applet has been created by Paolo Eustacchio.
The Szilassi polyhedron has 14 vertexes, 21 edges, and a hole. Like the tetrahedron, it has the remarkable property that each of its faces touches all the other faces. As a result, it requires seven colours to colour each adjacent face, providing the lower bound for the seven colour theorem on toruses.
A stainless steel sculpture model of the polyhedron can be found in Beaumont de Lomagne, France, in Pierre de Fermat's house, since 2002.