Solid body with plane

Hi
I have a problem with a circuit for the university.
I have a solid body, which it is to be divided into levels. Then they should  get a thick yet.  It Should then be placed in each body on the plains, which have a certain distance from the edge of the flat. I have a circuit, but the problem is the missing plane there and also some body. I need help relatively quickly.
to the system:
I work with Rhino 5 and Grasshopper version 28/09/2012, build 0.9.0014

here schematically
the black bar should be flat and gray, the body thereon