how much entropy is there in the shape of a rock? If I dig up a given rock, make a 3d model of it, and compare that model with those of a large number of other rocks from the same area, what fraction of other rocks would have the same 3d model?

Let's say that the measurement is performed with an accuracy relative to the size of the rock, so a rock that fits within a 100cm sphere might be measured to within the nearest centimeter.

It would be fine to only look at rocks that have been through similar geological processes, rather than all rocks in an area.

I'm broadly interested in an answer for all land areas on Earth, but if there's data for some small region, or theories about rock shape that allow estimating the average entropy, that would be a useful answer.
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.