Hi Rudl, check out the attached 3DM file for an example of how to solidify your object to get that sort of result that I think you want.

I duplicated the edges of the your top surface there by copy/paste, then flattened them down using the edit frame in a side view so that they would form a planar bottom face, then drew connecting lines up and built planar walls for the sides with Construct > Planar:




Now that the object is a solid, the "side walls" are existing in the object for generating a shell - select all the side-wall and the bottom faces for the openings:




Then run Construct > Shell, and those areas will become openings, while the unselected faces remain in place. That produces a result like so which I think is close to what you want:




Again the key difference here from what you were trying to do earlier is having a solid result where there are "side walls" adjacent to the surfaces that will be offset during the shell operation. When you try to thicken an open surface, the thickener does not know how to build any kind of side walls other than ones at a 90 degree angle to the surfaces, and that's one of the biggest reasons why you'll get a different type of result in that case.

Starting with an open surface tends to work best when you are thickening only a single surface, or with multiple surfaces if they are all smoothly connected by fillets, or have a symmetrical arrangement. If you have something other than those cases, you will probably want to form a solid out of your shape first before doing the shell. Then basically the side walls of the solid will be inherited down into the shape of the shelled result.

Hope this helps!

- Michael