Any Eggsplanations for this?

At a recent meeting Cath brought out an egg (or was it?) for our inspection.

It was sort of egg-shaped, although a little more symmetrical than most bird eggs. It seemed to have pores and felt light(ish) and was hard. Discussion ranged around turtle eggs, bird eggs, Cadbury Cream Eggs, oddly worn stones, or unusual fruit stones. It floated in water. Finally we cut it open whereupon it disintegrated into a shower of shell pieces and some crystalline matter which it contained, filling just a small proportion of the interior.

We were still none the wiser – so if anyone has any ideas here are some images, including microscope images of the shell and interior matter.

All suggestions welcome.