Hi James and Friends
I saw your file, ingenious enough to create
a thicker along the edges of the polygons, then working
with the boleans we will get what we want ...
but it still does not work ...
In any cases where we want an integral polygon, we can not do it
because the connecting lines of the centers with the midpoints
the edges of the triangles intersect each other ...
even more if the mesh of the triangles and pretty uneven
here:
http://www.mediafire.com/file/1pf6zo59nkj5uq1/VORONOI.zip/file
you will find files that will better illustrate the problem,
I have also worked on your file, deforming the triangular mesh a little
and trying to lower the size of the line
(Sweept profile) but, under a certain value you can not go,
and so, as you will see, the result is not ,according to me, yet
satisfactory
have a nice day
al