A rendering of the proposed National Sofa, to be located across Pennsylvania Avenue from the White House. (Copyright James Allegro, AIA and Doug Michels)

Have you ever taken a walk through Lafayette Square and said to yourself, “You know what this place could use? A 300-foot marble couch, facing the North Lawn of the White House.” You and me both! Thankfully, dreamers like us can check out what might have been at the National Building Museum’s “Unbuilt Washington” exhibition, opening Saturday.

All kidding aside, the exhibition is a fascinating showcase of alt-reality visions of iconic D.C. landmarks, along with wisely unbuilt architectural missteps, including the National Sofa, which, if realized, likely would have become the world’s largest outdoor sleeping quarters.

The drawings and photographs in the collection are drawn from the Library of Congress, the National Archives and private firms that dared to dream big but whose ideas were ultimately overlooked. You’ll see a proposed version of the Kennedy Center that was saucer-shaped, a Tudor-style Library of Congress and a proposal for an executive mansion on Meridian Hill highly reminiscent of Rome’s Imperial Palace.

The exhibition is open through May 28. Admission is $8 for adults, $5 for ages 3 to 17, students and age 65 and older, and free for age 2 and younger. Below, see alternate visions for the Lincoln Memorial, the Capitol and Memorial Bridge.

Proposal for the Lincoln Memorial by John Russell Pope, 1912. (National Archives)