Herschel's Enneahedron
The coordinates of this family of polyhedra were found by Christian Lawson-Perfect and Michael White (see this Aperiodical article and this Numberphile video). The polyhedra have nine faces and 11 vertices. It has one degree of freedom; use the slider for the parameter a to see the various polyhedra.
What's special about this family? The net of these polyhedra is the Herschel graph: the smallest non-Hamiltonian polyhedral graph.