How to make polysurfaces from these hexagonal curves

Is there anything to loop each hexagonal curve so that all the curves can be patched with polysurfaces?
Or is there any other ways to unroll these curves as I just want to flatten these curves and get to laser cut them?
Thanks a lot!!

soft (22.6 KB)

Like this? soft (16.8 KB)

If you want them flat, the shapes of the curves need to change quite a lot.
One simple way to do this is using intersections of tangent planes:
soft (37.5 KB)