The cube octahedron was one of the favourite polyhedra of Buckminster Fuller. He even gave it a special name: "vector equilibrium", because among all regular or semiregular polyhedra it is the only configuration in which the length of each edge is equal to that of the radial distance from its center of gravity to any vertex.
The two pictures below are identical. A few strings are painted black in the right picture, just to make the cuboctahedron more visible. The inside of the structure is a perfect icosahedron.
According to Bucky the vector equilibrium (he even spoke about "our friend the vector equilibrium") was not only a structure but could also be seen as a system. From Amy C. Edmondson'sA Fuller Explanation I took this typical Fuller sentence:"The vector equilibrium is a condition in which nature never allows herself to tarry. The vector equilibrium itself is never found exactly symmetrical in nature's crystallography. Ever pulsive and impulsive, nature never pauses her cycling at equilibrium: she refuses to get caught irrecoverably at the zero phase of energy."
Below again two identical pictures of a cube octahedron, but now with a larger icosahedron inside
The small icosahedron inside: