Cavities and Computing Their Volumes

Identify the cavities Each connected cluster of Voronoi polyhedra vertices and edges that avoid overlap with the exclusion spheres in the system identifies a distinct cavity of available space. 

Identify the Delaunay tetrahedra enclosing the cavities The union of the Delaunay tetrahedra corresponding to the aforementioned cluster of 

Voronoi vertices completely encloses the associated cavity. This union volume provides an upper bound of the cavity s volume. 

Determine the actual cavity volume and surface area within the Delaunay tetrahedra The overlap of the exclusion spheres with the relevant Delaunay tetrahedra is subtracted analytically, leaving only the actual cavity volume and surface area. This nontrivial calculation is from the multiple overlap of exclusion spheres, but a systematic method for carrying it out is available.70 71 

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