Our interest here is how available low-energy structures with controllable shapes are. For example, the shape maps for Tet 6 Di and Tri 8 Di tell very different stories about the shape diversity over their stable structures. For the application of binding/separating isotropic guests, an ideal (symmetric) shape is useful. However, precisely controlled binding environments are often asymmetric, and controlling the cage and pore's shape (and dynamics) is critical to designing enzyme-like hosts.