Generally speaking, it’s not a good idea to walk around while looking up, but that’s exactly what you’ll need to do to appreciate a new installation at the Renwick Gallery called “Parallax Gap.” Created by architecture firm FreelandBuck, the piece consists of nine different illusions that click into place only if you stand at the exact right point underneath each of them and gaze upward.

“We want people to wander through this room and really figure out this puzzle for themselves, while also enjoying this wonderful, confusing, complex shifting of patterns and geometries,” Renwick curator-in-charge Abraham Thomas says. “Touch wood, there won’t be collisions.”

When you do find one of the nine sweet spots, you’ll see a re-creation of an iconic American ceiling floating above you — ceilings from buildings including San Francisco’s Palace of Fine Arts and D.C.’s Eisenhower Executive Office Building, which is across the street from the Renwick. “Parallax Gap,” however, doesn’t aim for realism. Rather, each ceiling is like a blueprint come to life — albeit one that’s purple and pink as well as blue.

Artists David Freeland and Brennan Buck created these illusions by printing stylized blueprints onto plastic fabric, and then using a machine to make precise cuts so viewers can see through one layer to the next one above it. The layers — between two and five for each depicted ceiling — were then fitted into metal frames and hung from the Renwick’s actual ceiling.

It’s a little strange for a museum devoted to craft — which usually means things made by skilled hands — to showcase a piece that was printed and cut by machines. However, computer-controlled printers and AutoCAD software are tools like any other, Thomas says.

“This is craft done at a digital level. It’s not handmade, but it’s still a culture of making that’s distinct from mechanized production,” he says. “Many makers right now are quite happy using digital tools together with the old analog ones.”

In addition to getting people to think about the definition of craft, the goal of the piece (which opened July 1) is to expose architectural illusions that you may see every day, says Helen B. Bechtel, the independent curator who coordinated the exhibit. For instance, many real-life ceilings feature a technique called “trompe l’oeil,” which uses painted-on shadows to create a sense of depth. In “Parallax Gap,” as you walk around, you can see how clever shading — printed by machine onto flat pieces of plastic fabric — has provided a similar illusion of depth.

“The most exciting thing for me isn’t where illusions click into place, but where they break down,” Bechtel says.

Renwick Gallery, 1661 Pennsylvania Ave. NW; through Feb. 11, free.