What happens at the edge of a diamond?

In a diamond, there is a regular 3D lattice of carbon atoms, right? In graphite, the atoms are arranged in rings. So far so good. At the edge of a piece of graphite, you just have one last ring. At the edge of a diamond, what do the last atoms of carbon bond to? Each other? Oxygen? What ever it is, it’s this compound (not diamond) that is used for etching, cutting glass etc, ‘cos it’s on the outside edge. So do diamonds have a harder-than-diamond coating??