how much entropy is there in the shape of a rock?
This would actually be an interesting research project.  The ability to do a 3-D scan and model of a rock's shape in a manner that is fast enough to get a statistically meaningful number of rocks measured is relatively new.  Certainly you can easily name things that probably control the shape of rocks (lithology, mode of erosion, mode of transport, history of these things) but saying something about this in a quantitative way has not been done AFAIK.

I think this is the sort of question that might result in surprising insights.  Or it might lead nowhere.  Certainly the question 'Does arid region erosion result in different shaped rocks than glacial erosion?'  answered in a quantitative way sounds worthwhile to me.