1. create the star with the create polygon tool (you've already done)
2. create a poly cube (again, done)
3. I used the poly split tool to get the star so that each face was a quad.
This took a minute of staring at it to get the idea for the
topology but it's not that bad.
4. In object mode, select the star then use the extrude face tool.
5. The extruded geometry should have faces on both side (also make sure you have keep faces together selected)
6. Once I had the depth I wanted, I just moved the star so that it intersected the cube.
7. Select the cube, then the star; then do a boolean difference (maybe selected them in the other order??? can't remember)
8. Render to your heart's content.