When I polish a marble floor I am having trouble with the edges of the tile being shinier than the rest of the floor. This shiny edge is a thin line running from one corner of the tile. It appears to be on the low side of the tile where my diamon

The shiny edges are what we call “v” edges, since they normally form a “v” along two edges of the tile. You are correct in that these “v” edges are areas that are lower than the adjacent tile and your diamonds are not touching these areas.
The best way to eliminate “v” edges is to flatten the floor but in this case where the customer doesn’t want to spend the money to flatten the floor you will need to blend these areas by learning how to polish and polish very well. Spend more time polishing and you can blend these “v” edges to an acceptable appearance.