Carbon cages in endohedral and exohedral fullerene derivatives are usually different. A recent report suggested that chlorofullerene C66Cl10:C-s and endohedral metallofullerene (EMF) Sc-2@C-66 shared the same cage C-#4348(66):C-2v, while it was denied by the definitive characterization of Sc-2@C-66, which actually possesses the C-#4059(66):C-2v isomer. Here, we show that a C-#4348(66):C-2v cage with a double hexagon-condensed pentalene (DHCP) moiety, which was captured by exohedral chlorination, is also capable of being stabilized by encapsulating tri- or divalent monometal (M) species. On the basis of density functional theory calculations combined with statistical mechanics analyses, C-#4348(66):C-2v-based mono-EMFs M@C-2v(4348)-C-66 (M = Tb, La, Y, and Yb) were demonstrated to be the most stable and predominant isomers at the fullerene formation temperature region, while another chlorinated cage C-#4169(66):C-s, featured with triple sequentially fused pentagon (TSFP) moiety, is less favorable to be obtained in the form of EMFs, although these two cages can be interconverted by a simple Stone-Wales transformation. The superiority of M@C-2v(4348)-C-66 over M@C-s(4169)-C-66 comes from the stronger interaction Of M-DHCP over that of M-TSFP in both ionic and covalent bonding aspects. In addition; size-selective complexation of host [n]cycloparaphenylene ([n]CPP) and Tb@C-2v(4348)-C-66 was simulated, showing that [10]CPP exhibits the best affinity toward Tb@C-66, which provides a new opportunity for isolation and characterization of C-66-based mono-EMFs.