The cuboctahedron most commonly emerges in the close-packings of atoms, particularly in the face-centered cubic metals, such as copper, silver, and gold. Notice that if you increase the atomic radii using the slider on the right that all the spheres touch at the same time, reflecting the efficient packing of atoms in these structures. Also, if you look down on any of the cuboctahedron's eight triangles or six squares you should see a very symmetrical arrangement. My friends in the Symmetry Squad can tell you more about this.