Voronoi on mesh/ surface

Dear All

I have now managed to generate a voronoi pattern on a morphed surface with the help of previous voronoi related posts... the thing is now to introduce a frame/ inner surface.  I have tried offsetting the original diagram, but it refuses to produce closed polylines... i have also tried dividing the curves and then using the interpolate curve to reconnect  an inner surface, but with no luck... could anyone please help me?

PS I have also looked at a voronoi project on the geometry gym website, but it doesn't want to open (it 'loses' the important components) even though i have the latest grasshopper release.

thanks