can you specify what you mean by "a random voronoi tesselation"?
Are you creating a 3D voronoi tesselation and trying to extract its edges?If so, Using voronoin /VoronoiDiagram functions output arguments,
returns matrix v which represent Vertices of edges and a cell array c where each element of c containes the row indices of the Voronoi vertices v that make up a Voronoi cell.
would return the vertices corresponding to cell number 'i'
Hope this helps!