Voronoi diagrams I see have few if any hexagons (use your favorite mathematical reference or image search). Is that idea that if the points are distributed equidistant in 'alternating' ranks [0], then the diagram is hexagons?
Also, what is "binary breakup" and "binary fracture"?
[0] Alternating ranks: I mean something like the following (is there a better name?):
. . . . . .
. . . . . .
. . . . . .
. . . . . .
The dots need to be the vertices of equilateral triangles for the Voronoi diagram to be hexagons, the above is a rectangular grid rotated 45 degrees.
You can overlay a regular hexagonal tessellation over a regular triangular tessellation to see this.
In context, binary breakup and binary fracture apppear to mean a splitting ofa whole into two parts along a given line or plane