The recession hasn’t stopped construction of Three Apartment Buildings On West 12th Street, between the Hudson River and Washington Street. Three factories on the block are being turned into the Related Companies’ Superior Ink development at 400 West 12th Street, developer Cary Tamarkin’s five-unit building at 397 West 12th Street and Flank’s 12-unit building at 385 West 12th Street. While the developers were able to keep construction going during the downturn, it remains to be seen how the new units will sell. Related reported that Superior Ink, which has 68 units and seven townhouses, was 80 percent sold two months ago, and designer Marc Jacobs bought a townhouse in the development for about $2,888 a foot. Flank says that seven of its 12 units are sold, but all the sales took place last summer. And at Tamarkin’s development, only one of five units have sold, and prices were cut by 15 percent in the building last month.