Starting Wednesday, 227 brand new affordable apartments are up for grabs at4275 Park Ave. in the Bronx. The residence, dubbed Park House, is a new construction designed byCOOKFOX Architectsand developed byBreaking Ground, a non-profit organization that matches low-income New Yorkers with homes. Park House is the first project undertaken by the organization and will offer energy-efficient studio, one-, two-, and three-bedroom apartments pricedbetween$494 and $1181 to qualifying applicants earning between 40 and 60 percent of the area median income.