This intriguing polyhedron was discovered in 1977 by Hungarian mathematician Lajos Szilassi. It has seven faces, 14 vertexes, 21 edges, and a hole. Each face is a six-sided polygon. Topologically, if it were smoothed out, it would be equivalent to a doughnut (or torus). You could describe it as a toroidal heptahedron.
Like the tetrahedron, the Szilassi polyhedron has the remarkable property that each of its faces touches all the other faces.
Photos by I. Peterson