Sting managed to circumvent the new mansion tax because he entered into a contract to buy the unit in June 2016. (The old rates were grandfathered in for contracts signed before April 1.) Last year he sold a duplex at 15 Central Park West for $50 million.

The other triplex sale was at the Marquand, a condo conversion on East 68th Street and a quick stroll from Central Park. The unit had been listed for $36 million.

Known as Penthouse East, the apartment encompasses 7,000 square feet on the 11th through 13th floors and features several large terraces, as well as a solarium and an exercise pool and hot tub on the top level. The four main bedrooms, each with a connecting bath, are on the lower level, including an enormous master suite, which has a large walk-in closet and a dressing room. There are also four fireplaces.

At 520 Park, another limestone creation by Robert A.M. Stern, full-floor condominiums on the 35th and 31st floors sold. The more expensive of the two, the unit on the higher floor, was initially listed for $35.6 million.

Each contains 4,628 square feet of space, with four bedrooms and five baths, along with spacious eat-in kitchens and family rooms. The identities of both buyers were shielded by limited liability companies.

The purchasers of an apartment on the 86th floor of 432 Park, the supertall skyscraper, between 56th and 57th Streets, were identified as the philanthropists Roger and Susan Hertog. The couple’s new 4,028-square-foot home takes up a half floor, and features three bedrooms, four and a half baths, a library and panoramic views of Central Park and the city skyline.