What is the best way to polish the edges and corners of a marble floor? The machine I use cannot fit into the corners.

The best way is not to polish them at all. Edges and corners rarely require any work since they are not subject to foot traffic. If for some reason you need to hone or polish them, there is a machine available that has a triangular pad that can get into the corners. These sanders can be purchased at most home centers.
TIP The best way to deal with edges is to blend into them by overlapping successive diamond grits. Stay at least eight inches away from the edge.