Perhydrogenation of icosahedral fullerenes larger than C₆₀ is predicted to produce thermodynamically stable fulleranes. The fulleranes are significantly stabilized by partial endo-hydrogenation, allowing nearly optimal sp³-hybridization for each carbon atom. Quantum chemical calculations show icosahedral fulleranes such as C₈₀H₈₀ and C₁₈₀H₁₈₀ to be less strained than any of the previously reported (CH)_n cages, including C₆₀H₆₀ and the experimentally known dodecahedrane, C₂₀H₂₀. The novel structural motifs of the fulleranes also apply for icosahedral diamondoids, which are composed of covalently bound carbon layers of the fullerane framework. The match between the layers is nearly perfect, resulting in low structural strain and high thermodynamic stability. The described structural characteristics of the fulleranes and diamondoids provide new insight into the structural variety of hydrocarbons. Furthermore, they are expected to aid in identification and characterization of the experimentally known hydrocarbon and diamond nanostructures.