Pulsed laser vaporization has been used to produce nanooctahedra of MoS2 and MoSe2. The nanooctahedra primarily form in two- or three-layer nested octahedra, although nesting up to five layers has been observed. Tilting the TEM sample stage and mapping how the images of single particles transformed provided the evidence to verify their octahedral geometry. Analysis of 30 two- and three-layered octahedra showed that their outer edge lengths clustered at similar to3.8 nm and similar to5.1 nm, respectively. This discreet sizing and the high symmetry of these closed nanooctahedra represent the closest inorganic analogy yet to the carbon fullerenes. The geometrical implications for forming octahedra from these layered compounds are investigated by considering different atomic arrangements assuming either trigonal prismatic or octahedral coordination around the Mo atom and yields two possible configurations for the actual structure of the nanooctahedra. A preliminary survey of pulsed laser vaporization of other layered metal chalcogenides shows that these dichalcogenides differ in their tendency to form small closed layered fullerene-like structures. These materials can be ranked from highest tendency to lowest as follows: NbSe2, WS2, WSe2, SnS2, TaS2, GaS, ReS2, and MoTe2.