For the first time, actinide endohedral metallofullerenes (EMFs) with non-isolated-pentagon-rule (non-IPR) carbon cages, U@C-80, Th@C-80, and U@C-76, have been successfully synthesized and fully characterized by mass spectrometry, single crystal X-ray diffractometry, UV-vis-NIR and Raman spectroscopy, and cyclic voltammetry. Crystallo-graphic analysis revealed that the U@C-80 and Th@C-80 share the same non-IPR cage of C-1(28324)-C-80, and U@C-76 was assigned to non-IPR U@C-1(17418)-C-76. All of these cages are chiral and have never been reported before. Further structural analyses show that enantiomers of C-1(17418)-C-76 and C-1(28324)-C-80 share a significant continuous portion of the cage and are topologically connected by only two C-2 insertions. DFT calculations show that the stabilization of these unique non-IPR fullerenes originates from a four-electron transfer, a significant degree of covalency, and the resulting strong host-guest interactions between the actinide ions and the fullerene cages. Moreover, because the actinide ion displays high mobility within the fullerene, both the symmetry of the carbon cage and the possibility of forming chiral fullerenes play important roles to determine the isomer abundances at temperatures of fullerene formation. This study provides what is probably one of the most complete examples in which carbon cage selection occurs through thermodynamic control at high temperatures, so the selected cages do not necessarily coincide with the most stable ones at room temperature. This work also demonstrated that the metal-cage interactions in actinide EMFs show remarkable differences from those previously known for lanthanide EMFs. These unique interactions not only could stabilize new carbon cage structures, but more importantly, they lead to a new family of metallofullerenes for which the cage selection pattern is different to that observed so far for nonactinide EMFs. For this new family, the simple ionic A(q+)@C-2n(q-) model makes predictions less reliable, and in general, unambiguously discerning the isolated structures requires the combination of accurate computational and experimental data.