as the euler characteristic suggests, the small cubicuboctahedron is a toroidal polyhedron of genus 3 (topologically it is a surface of genus 3), and thus can be interpreted as a (polyhedral) immersion of a genus 3 polyhedral surface, in the complement of its 24 vertices, into 3-space. (a neighborhood of any vertex is topologically a cone on a figure-8, which cannot occur in an immersion. note that the richter reference overlooks this fact.) the underlying polyhedron (ignoring self-intersections) defines a uniform tiling of this surface, and so the small cubicuboctahedron is a uniform polyhedron. in the language of abstract polytopes, the small cubicuboctahedron is a "faithful realization" of this abstract toroidal polyhedron, meaning that it is a nondegenerate polyhedron and that they have the same symmetry group. in fact, every automorphism of the abstract genus 3 surface with this tiling is realized by an isometry of euclidean space.