The geometries of fullerenes are governed by the isolated pentagon rule (IPR), which states that stable fullerenes have each of their 12 pentagons surrounded by five hexagons. At the dawn. of fullerene science, it was widely believed that the IPR would also be applicable for endohedral fullerenes. In 2000, that idea was altered by the discovery of the first non-IPR fullerenes, Sc-2@C-66 and Sc3N@C-68. The structural data for Sc-2@C-66 ere interpreted to indicate the presence of a pair of doubly fused pentagons. However, that structure has remained a long-standing mystery, since it is thermodynamically unfavorable. Here, we demonstrate definitively that Sc-2@C-66 does not have the structure that was long believed to be but a brand new type. 2D NMR spectroscopic and single-crystal X-ray analyses disclose that Sc-2@C-66 has a C-2 nu(4059)-C-66 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.