The shine on our travertine marble floor has not looked even since it was installed. Many areas have dull spots. The installer told us this was characteristic of the stone, but I’ve noticed that a local hotel has the same travertine, and it loo

Your installer is correct. Most travertine contains many holes that are filled with a cement filler. The cement filler does not take a shine when polished—hence the dull spots. The floor you observed at the hotel has probably been coated with a wax or made uniformly shiny through some other coating process. I would not recommend this for your home. A hotel spends every evening polishing and or waxing the travertine floor to maintain its shine; unless you would like to do the same, I would advise against it.