What type of structure do metal atoms form surrounded by a solid piece of the metal?
Metallic bonds are formed when large pieces of metal atoms are formed together. The bond itself is called an "electron marine," where electrons are equally shared by all atoms contained by the metal, free to float about as water would contained by a bucket or... a water balloon. If you bend the metal, the electrons flow into the new position and hold, giving the metal it's malleability or ductility, much approaching how the water balloon keeps a shape when squeezed.
The structure itself is call an electron sea through a metallic bond.