A new aluminate Sr33Bi24+deltaAl48O141+3delta/2, having an F43m cubic structure (a = 25.090 Angstrom, Z = 4) and forming a close packed face centered cubic array of "Al-84" fullerene geometry, has been discovered. This original structure consists of corner-sharing AlO4 tetrahedra forming "Al84O106" cubic units whose assemblage delimits five types of cages, three of them being empty, one being occupied by strontium, and the fifth one forming the huge spheric fullerene-type cavity. In the latter, strontium, oxygen, and bismuth ions form concentric spheres, with an onion-skin-like configuration. The latter ions are disposed into a compact "Bi16O52-(n)rectangle(n)" anion whose the exceptional geometry is characterized by a strong stereoactivity of the 6s(2) lone pair of Bi3+.