Hi 4rw1n, also on something like that it can work better to make a solid and then shell the solid rather than trying to thicken an open surface. With a solid shell the shelling mechanism gets to intersect extended surfaces with "side walls" which tends to work better. When you thicken an open surface it's a pretty different process which has more difficulties with surfaces all at different angles to each other.
I've attached a result of making your object into a solid and then shelling it. There was still an error in one spot where you had a thin pointy piece which I had to fix up manually.
Also I made all the main pieces using Construct > Planar rather than Network, that should also help with offsetting and shelling work since it will make trimmed analytic plane surfaces rather than general surfaces.
- Michael
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