Opengl boolean subtraction

Question

Is it possible to do Boolean operations between polygons?

I want to do a figure like this in OpenGL and I thinking of doing it with a sphere and four subtractions with four smaller spheres.

Answer 1

No, that's not possible with just OpenGL.
OpenGL is a very low level API. it allows you to display polygons and that's about it.

What you're describing is usually done in the application level above OpenGL.
Look at the bottom of this article for some references on libraries that does that:

http://en.wikipedia.org/wiki/Boolean_operations_on_polygons