Making a a polygon inside a polygon.

Is it possible to cut a circle into a polygon.

well circle are n sdies polygons

just specify the segment qty in panel

salutations

I don’t mean like that. Im trying to hollow out an object so that there is a hole in it in the shape of a cylinder.

Not the most elegant way but try the boolean modifier
http://wiki.blender.org/index.php/Doc:Manual/Modifiers/Mesh/Booleans

Another approach to this situation would be to do things in reverse. That is, instead of trying to create a void within a solid, model the void first and put the solid around it.