Überoctoplex

The Überoctoplex is a certain polyhedron with the property that with a light placed at every vertex, it is not possible to illuminate the entire interior of the polyhedron (a three-dimensional variant of the ). It is the smallest known polyhedron with this property by face count and by vertex count. The figure can be realized as an isogonal polyhedron with pyritohedral symmetry.

It is abstractly identical to the rhombicuboctahedron. Pairs of vertices can be merged to form Jessen's icosahedron.