Proper Travertine Cleaning & Polishing
Acids will cause etching of your travertine. What happens is the acid in the vinegar eats away at the calcium carbonate in the stone, producing small scratches that make a dull spot on the travertine where dirt and grime are attracted and absorbed. This etching reaction is nearly instantaneous, no matter how much water you dilute the vinegar with. A penetrating sealant can limit the acid from penetrating deeply into the stone so that etching remains superficial and can be buffed out, but this is not a viable solution.
The best way to clean travertine is with a quality cleaner that is neutral in pH. You can use a mild liquid dishwashing soap, like Dawn, but make sure it is plain, with no fancy additives or “freshening” aromas.
Travertine Floor Cleaning
The same goes for travertine floor cleaning. Be vigilant about any mud and dirt tracked into the house; have a strict Take Your Shoes Off at the Front Door policy.