On Aug. 15, Columbia University Medical Center students and faculty will begin using the description-defying Roy and Diana Vagelos Education Center, designed with a brazenly asymmetrical southern half by Diller Scofidio + Renfro. On the southern half of the 14-story building, all the floors cantilever and half of them slope; much of the 100,000-sq-ft building’s concrete structural system is exposed. That posed myriad challenges for the structural engineer, Leslie E. Robertson Associates, and the contractor, Sciame Construction LLC, which said the superstructure took 50% longer to build than a regular, repetitive job.