The isolated pentagon rule (IPR) states that stable fullerenes have each of their 12 pentagons surrounded by five hexagons. On the contrary, in 2000, that idea was altered by the discovery of the first non-IPR fullerenes, Sc2@C66 and Sc3N@C68. Themolecular structure of Sc2@C66 was assigned to possess a C2v(4348)-C66 cage that contained two sets of double fused pentagons by using 13C NMR spectroscopy and powder X-ray diffraction data analysis. However, that structure has remained a long-standing controversy, since it is thermodynamically unfavorable. Here, we demonstrate definitively that Sc2@C66 does not have the structure that was long believed to be but a brand new type. 2D-NMR spectroscopic and single-crystal X-ray analysis disclose that Sc2@C66 has a C2v(4059)-C66 cage containing two sets of unsaturated linear triquinanes (ULTs), in which three pentagons abut one another and two scandium ions are located within the folds of each of the ULT units. Our identication of Sc2@C66 as Sc2@C2v(4059)-C66 shows that new motifs in carbon cage geometry continue to be discovered and calls attention to the ULT unit, whose aromaticity and coordination chemistry deserve further study.