A saddle‐shaped π‐extended zinc porphyrin containing a peripheral pyridyl ligand undergoes quantitative self‐assembly into a cyclic trimer. The trimer has a prismatic structure with negatively curved side walls, which promote the formation of supramolecular organic frameworks stabilized by dispersion interactions. The first framework type, UWr‐1, has the npo topology, with a hexagonal structure analogous to the Schwartz H triply periodic minimal surface. Co‐crystallization of the trimer with either C60 and C70 produces the isomorphous cubic UWr‐2 and UWr‐3 phases, characterized by the ctn network topology and a structural relationship to the Fischer–Koch minimal surface S. All three phases contain complex labyrinths of solvent‐filled channels, corresponding to very large probe‐accessible volumes (68% to 76%). The UWr‐2 network could be partly desolvated while retaining its long range dimensional order, indicating remarkable strength of the dispersion interactions in the crystal. A theoretical analysis of noncovalent interactions shows the role of geometrical matching between the negatively curved porphyrin units and positively curved fullerenes.