Hi Pilou, it's going to be extremely difficult to try and calculate a thickened shell for a shape like that with so many little fragments to it especially with the fragments touching each other at slightly sharp creases. When you have pieces that meet each other at a sharp crease, the offsets of each surface do not touch each other and that then involves trying to extend and intersect the offset surfaces which can be a complex calculation.

It's further made more difficult by having many surfaces made up of surfaces with one side squished down to a single point in order for the surface to have 3 sides. It actually still has 4 sides but one side is degenerate and such a surface is difficult to extend along either edge that touches the collapsed point area.

So it's just a tremendously difficult thing to try and offset very well in a CAD program.

Maybe your best bet is probably to convert it into a polygon mesh format and use a mesh offset function in a polygon mesh editing program.

- Michael