Frank Woolworth famously built an empire on five-and-dimes. Now, for a considerably larger sum, New Yorkers can own a piece of his very American legacy. The top 30 floors of the Woolworth Building are being converted into luxury condominiums by Alchemy Properties and architect Thierry Despont, who has drawn the 34 half- and full-floor apartments (including a five-level pinnacle penthouse) along generous prewar lines in a rich cream palette accented with custom maple paneling and the original “W” motif. “Cass Gilbert created the skyscraper archetype,” says Despont. “We’re bringing it back to life.” Apartments start at $4.6 million;Woolworth Tower Residences Sales Office, thewoolworthtower.com.