Methods of the Delaunay and Voronoi tessellation are applied to investigate significant structures and structural differences among liquids, glasses, and crystals of the softhyphen;core (inverse 12th power potential) and hardhyphen;core models for which molecular dynamics (MD) techniques are used. With particle configurations obtained by MD simulations the Delaunay tessellation for the three dimensional systems defines uniquely a network of tetrahedra. Density dependent properties of the irregularity distribution which measures the magnitude of distortion of each Delaunay tetrahedron (DT) from regular shape (equal edge lengths) and of the length of edges of DT are examined in detail for both models. Clear differences between the hardhyphen;core and softhyphen;core systems are observed. Short range correlation of DT is calculated on the pair distribution function of centerhyphen;tohyphen;center distances of the circumspheres of DT, which turns out to be useful to distinguish the short range order of glasses from that of crystals or liquids. It is also shown that there are no clear differences in the distribution of various types of Voronoi polyhedron (VP) between liquids and glasses. However, among various types of polygons (ihyphen;edged faces) of VP, the contribution fromi=5 increases rather rapidly with increasing density around the glass transition point.
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