If it were possible for a bunch of bricks and stone to be embarrassed, the National Gallery of Art’s East Building should be blushing right now. After all, like a highfalutin fan dancer, it’s stripping down to its nakedness in front of everyone.

But I prefer to think of what’s going on over near the Mall not as burlesque but as performance art. Call the daily show “Calloused Hands and iPads: How Do You Keep the Walls From Tumbling Down?”

Well, perhaps “tumbling down” is a bit melodramatic, but here’s what’s happening: In 2005, the pink marble panels that envelop I.M. Pei’s stunning museum started to show worrying symptoms. Excess mortar and lead shims had inadvertently tied the stones together. Instead of each being able to float freely over the brick and concrete wall behind, they were locked to one another. As temperatures rose and fell over 30 years, the fastening system failed. Stones started to pull away from the building.

It is a bad thing to have stones pulling away from a building. Flatten a single tourist with a 450-pound slab of falling marble and people talk. And so a challenge was issued: Who can fix this?

The response came from people such as Lenny Pagliaro, a mason and one of a team of contractors who have come together to take off all 17,000 stones, refinish them and put them back in exactly the same places. It’s an $85 million project that won’t be finished until 2014.

Pablo Garcia, a mason’s helper with Pagliaro/Lorton/Nardi. LLC., puts a marble panel back in place at the National Gallery of Art’s East Building. (John Kelly/WASHINGTON POST)

“This is the largest stone job I’ve ever worked on,” Lenny told me as I toured the site late last year.

Contractors Balfour Beatty and Smoot Construction joined forces to execute the repairs, along with masonry contractor Pagliaro-Lorton-Nardi and the design firm Robert Silman Associates. It was a challenge just to come up with a way to do it. For starters, the museum has to remain open for the duration. It’s sort of like unbuilding the Great Pyramid of Cheops and then rebuilding it — with Pharaoh watching.

Then there’s the little matter of making sure what happened once doesn’t happen again. The marble cladding is attached with various anchors, and each panel is supposed to be free to move independently. Engineers came up with a sophisticated set of components to replace the old method, along with a soft silicone gasket that won’t stress the stones. Then they built a training facility in Bowie just to test the technique and teach workers how to use it.

Eleven months into the three-year project, they have it down to a science. Three types of scaffolding surround the East Building. Elevators take workers and equipment up and down the eight-story facade. Each stone is photographed, measured and given a number that indicates where it came from. It also gets a barcode and is scanned with an iPad. Stones are removed and placed in cradles that slide along a monorail. (When the stones were pulled off one section, a graffito was revealed: “Pittsburgh Steelers #1,” probably spray-painted by an ironworker in 1975 or ’76 as the building was going up.)

In Lenny Pagliaro’s masonry shop the stones are cleaned and milled: Bumps are ground down, depressions filled in. The aim is to take 50 stones off the building each day, send 50 stones through the shop and put 50 stones back on. As stones wait their turn, they rest in serried ranks on huge metal shelves.

At times, all the equipment around the museum — the scaffolding, the monorails — looks like a Mark di Suvero sculpture. It’s hard to detect Pei’s sublime design.

It’s a design that over the years has drawn countless hands to the dramatic knife’s edge on the building’s southwest corner. There’s something about that severe, 19-degree angle that just makes you want to touch it. So many people have touched it that the marble there has been polished to a sheen by the oil in their hands.

As I toured the site, I voiced my concern that the shiny patch would be scrubbed away in the stone shop. Not to worry, said Susan Wertheim , the gallery’s chief architect. It will get only a light cleaning. “We didn’t want the stones to look brand new,” she said.

You may not be able to touch the Picassos or Pollacks inside the East Building, but eventually you’ll be able to again touch the biggest masterpiece of all: the building itself.

To take a video tour of the East Building’s exterior renovation, go to www.washingtonpost.com/local. To read previous columns by John Kelly, go to washingtonpost.com/johnkelly.