Oct 27 (Reuters) - Fashion company Rent the Runway gained a fully diluted valuation of $1.7 billion after its shares opened nearly 10% above their offer price on Wednesday, becoming the latest consumer-facing business to ace its market debut in the United States. Shares of the Brooklyn, New York-based company opened at $23, up from its initial public offering price of $21 apiece. Reporting by Niket Nishant in Bengaluru; Editing by Maju Samuel