Hope you sealed the travertine when it was forst installed. You will need to renew the sealant at least every 6 months. Not cheap but it will prevent ugly stains and discolorations from "setting" into the porous stone.
Dishwashing detergent might be one of the worst cleaner to use. Not because it'll wear the stone, but because it produces too many suds and will leave a dulling film. Find a cleaner that is intended for stone, it'll also have the right ph so no damage.
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