This is a beautiful 8.9" fossil nautilus (Cymatoceras) from the Cretaceous aged formations of Madagascar. It is polished to highlight the details. These nautiloids are much rarer than the ammonites so frequently seen.
The shell of a Nautilus is made up of two layers. The inner layer has the iridescent shine while the outer layer provides protection from external forces. Inside the shell are septa which divide the living area of the shell into compartments and help the animal maintain balance and position in the water column.
Nautilus are "living fossils" in that species similar to this one still exist in our oceans.