Hi Wim - Network needs to be able to organize the curves into a 2D grid, so it has to have one set of "columns" and another set of curves that cross that for "rows". You won't be able to use network on 6 lines that touch each other end to end in a ring like you've got here because those don't form distinct rows and columns.

Maybe a couple things you could try would be to build it with sharp edges initially and then put in blends, see attached 3DM file. Or another possibility is to try putting in several horizontal sections and using Loft with the Loft style = "Loose" option, something like this: http://moi3d.com/forum/index.php?webtag=MOI&msg=8302.4

If you want it to look a lot like it's bubbling up from a plane you could try making a heightfield bitmap and using ZSurf:
http://moi3d.com/forum/index.php?webtag=MOI&msg=602.7

Also if you extrude your lines downwards and then delete the lines, then select the edges and run Construct > NSided that might give you a good result like this:







I think that the Nsided way might be the closest to what you're describing with not having creases but still having a sharp hex bottom shape.

- Michael