- MoS2, a layered compound with tribological and catalytic applications, is known to form a range of hollow closed nanostructures and nanoparticles, including graphene-like structures. These have been demonstrated experimentally through high-temperature synthesis and pulsed laser ablation (PLA), and theoretically with quantum chemical calculations. The smallest allowed structures are nanooctahedra of 3 to 8 nm size. Nicknamed the “true inorganic fullerene” in analogy to carbon fullerenes, they differ from larger multiwalled MoS2 fullerene-like nanoparticles both in their morphology and predicted electronic properties. The larger fullerene-like particles are quasi-spherical (polyhedral) or nanotubular, typically with diameters of 20 to 150 nm. Above a few hundred nm in size, these nanoparticles transform into 2H-MoS2 platelets. Fullerene-like particles have been recognized as superior solid lubricants with numerous commercial applications, and MoS2 nanooctahedra may have catalytic applications. Understanding the fundamental commonality of these two morphologies might prove essential in the development of new materials. The research on hollow MoS2 nanostructures of minimal size (< 10 nm in diameter) was initiated in 1993 upon the first independent proposal of the formation of nanooctahedra of MoS2 [3,5] (and BN) with six rhombi in their corners. In 1999, it was demonstrated that twoto four-walled MoS2 nanooctahedra, 3–5 nm in size and up to ca. 10 atoms, could be obtained by PLA. Similar results were subsequently reported in Ref. [1, 2] as illustrated in Figure 1a. Recent studies of high energy density methods such as laser ablation and arc– discharge resulted in small structures with only a limited number of atoms: Mo–S clusters or double-walled nanooctahedra.