You maybe remember from Nekyia that Hades has a rock collection. Apparently Hermes couldn't keep his hands off from it when he last visited the Underworld.
That is an orthoceras fossil. I must confess, though, that I'm not 100 % sure that those could be found in Greece. I've read in The First Fossil Hunters by Adrienne Mayor that small marine fossils in limestone early attracted attention in ancient Greece and correctly were perceived as evidence of former seas. But I don't know if orthoceras were among those fossils.
Of COURSE Hades' favorite rocks would be fossils!