Hi Lestatdelc, you might try offsetting just the Network surface all by itself - don't join the planar top to it because that makes for a much more difficult offset calculation. It's more difficult because the surface that Network generates won't be totally smooth to the planar top at all areas. It will be smooth at the curve stations but not in between those areas. Offset surfaces will only naturally touch each other if the surfaces being offset are smooth to each other. If not smooth they have to be extended and intersected and that can be difficult when they are close to being smooth but not quite, that makes for a shallow intersection.

Also you might try using Sweep instead of Network for this case - the way sweep works keeps more rigidity to the profile shapes as they travel along the rails, see the attached version generated with sweep which can be offset ok I think. Network is more of a fully bidirectional thing and will be a little more like a soap bubble kind of very slightly flattening out in areas away from the input curves.

I also took a look at the issue you showed with the inexact Network result - the actual distance in the area I zoomed into is 0.000008 units, so it's a very small difference and well below the 0.001 fitting tolerance level. It's normal for many types of generated geometry to have that small level of deviation in them from the original inputs. Many operations use an iterative refinement type mechanism for generating shapes and refine the results until they are within a tight enough tolerance of the original. So that's a normal and expected type of result.

I'm not quite sure of the final shape you're trying to get here, maybe if you described a bit more about how you want your final result formed (like is there an opening at the top or not) I might be able to give some more advice.

- Michael