The recently isolated first lower fullerene C-36 is computed primarily at the B3LYP/6-31G* level with some information derived from the semiempirical SAM1 method. Twelve low-energy cages are considered both with fullerene (pentagons and hexagons) and "quasifullerene" (also squares and heptagons) structural pattern. The B3LYP/6-31G* evaluations of the equilibrium isomeric composition at high temperatures agree well with the recently reported solid-state NMR spectra. The fullerene cage with a topological D-6h symmetry, that dominates at high temperatures, undergoes a small Jahn-Teller distortion. Some features of C-36-related nanotubes are also discussed.