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 non-self-intersecting 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. If the rectangles are collapsed into edges, Jessen's icosahedron is formed if the proportions are appropriate.