How I can solve the broken edges of Voronoi in grasshopper?

The boolean toggle input is not really a correct input for the pipe ends. You’d use a slider with a domain from 0 to 2. Yes your button outputs a ‘1’ but round ends are better since it creates less gaps at the pipe ends compared to flat ends. Creating a union of so many pieces will fail in most cases. It could be done using a loop but to be honest, I think it would only be a proof of concept and nothing more since a lot of print software can handle overlapping geometry.

As I wrote above, the result does not necessarily be unioned into one single object. If you need a single closed polysurface, for whatever reason, you will have to clean up your curve network, which can be done but is complicated.

Two useful topics on voronoi:

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