The exhibition, which will remain on display at least through October, sheds light on this often-overlooked aspect of the history of tall buildings with models, diagrams, photos, drawings, and videos.

In 1956, Frank Lloyd Wright designed The Illinois — intended to be the world’s first mile-high skyscraper. Stretching to 528 stories, and with parking for 15,000 cars and 100 helicopters, The Illinois ...