Systematization of the crystal structures of metal-rich chalcogenides was attempted with emphasis on the coordinations of a few key metal atoms.This approach gave a more complete interpretation of many chalcogenide structures, notably those of Ta2S, Ta 6S and Nb 2Se, than did the conventional descriptions using the packing of the coordinations of the chalcogen atoms.The pursuit of this approach led to the recognition of a polyhedron, which, owing to its repeated presence in many metal-rich compounds, appeared to be of great importance in crystal chemistry.It is a two-centered polyhedron formed by the interpenetration of two C. N. 14 Kasper polyhedra in such a way that the center of one of the Kasper polyhedra is the apex of another.The presence of a very short interatomic distance between the two centers is one of the important features of this polyhedron.With the help of this polyhedron as the building block, the structures of Zr 9S2 , -V3S and 0-V3 S were satisfactorily described and correlated; the short interatomic distances in the structures could be explained semi-quantitatively; and the structural differences expressed by the different packing schemes of the polyhedra and the 7