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

The inside is an inverted pyramid, to avoid overhang issues, and because a co-worker said it would be cooler. I included the ipt file, in case anyone wants to play around with it.

The stl has the hat at its full 10" diameter size, but I could only print it at 6" across, because of my print area. Fortunately, it's about the right size for a very ornery cat.