It turns out that, based on the research being reported in the article, a top-heavy pyramid appears to be better at straightening itself out when it is floating on a stream of air from below.
The researchers placed hollow paper pyramids inside the cylinder. The objects were about 1 to 5 centimeters high and were made of tissue paper or letter paper on carbon fiber supports, like tiny homemade kites. Physicist Bin Liu led the experiments, attaching a beadlike weight to a post running down the center of the pyramid and changing the height of the bead to give the object a different center of mass. Common sense says that the pyramid should be most stable when the bead is at the bottom of the post, like ballast in the hold of a ship. But when the team released the pyramids over the subwoofer, the opposite was true: The bottom-heavy pyramids were likely to flip over and fall, whereas the top-heavy ones remained upright and continued to hover (see first video), the group reports in an upcoming issue of Physical Review Letters.The video is available in that link. I'll keep an eye out on PRL and update this entry when I have
the exact citation for the paper.
Edit: We have a synopsis of this work AND the exact reference to it.