I drew a quick sketch of something I'm trying to achieve. The center feature is detailed and important - the square is just a basic concept.

I'd like to image that I have 2 (or more) of these parts and want to be able to stack them within one another (similar to a stack of cups).

But I can't figure out how to: 

1) fill in the gaps around the center "star" feature

2) how to properly get the shelling of that same "star" feature on the "inside". I'd like the wall thickness to be .012", but when I use the shell feature, it doesn't work as expected. I attached a screenshot of when I use shell, but I can't have that wall around the diameter - everything should be flush to the "bottom" of the box, minus the "fins" that will stick up, of course.

I hope that makes sense. Any insight?