Earth star fungus, probably Geastrum coronatum, with what appears to be a lid or protective cover detaching itself from the sporocarp, the spherical structure containing the spore-creating gleba.
I’ve never seen anything like it before, nor any reference to anything similar in my collection of Field Guilds or online – possibly because I haven’t looked hard enough.
Seen again five days later. The “lid” was raised higher, but still not separated from the rest.