Washingtonians are fortunate to live with the best of I.M. Pei’s architecture, the East Building of the National Gallery of Art. Opened in 1978, it set an extraordinarily high standard for designing new, modernist additions to traditional, classically styled buildings. It solved so many problems with such grace that it’s easy to take for granted just how good it is. There is no better way to honor the legacy of Pei, who died early Thursday at 102, than to spend some time in this magnificent space.

But first, look at it from the outside. One of the biggest challenges Pei confronted was the site itself, a four-sided, blunt wedge of land, bordered on its longest side by Pennsylvania Avenue and on its shortest side by Third Street, which looks onto the grounds of the U.S. Capitol, and the Reflecting Pool at its base. Pei had to create something that extended the east-west energy of the old West Building (designed by John Russell Pope), which fronts onto Constitution Avenue, yet presented a dignified face to Pennsylvania Avenue, which runs at an angle to the city’s rectilinear street grid. He was dealing with a problem that often confounds architects in Washington, where Pierre L’Enfant’s 1791 street plan chops up what would ordinarily be rectangular spaces into triangles.

It wasn’t just the odd, quadrilateral shape of the plot that presented difficulties. The addition also had to present a meaningful face to the building it was joining. And this is, for many visitors, the ultimate triumph of the design. When you emerge from the West Building, which was designed and built in the late 1930s, you look across a low, open plaza at the East Building’s mostly symmetrical facade, which looks like an exercise in strict, perspectival drawing. The two tower forms on each corner are angled sharply into the center of the space, framing the third tower in the distance. The play of angles concentrates the visual energy into the building itself, a bit like how a drawing made in strict one-point perspective seems to suck the eyes into a hole in the middle of the paper.

Seen in the late afternoon, the Tennessee marble glows like the light raking over an Italian hill town, and the forms seem to match. The building is monumental but retiring, forceful but not overbearing. The entrance, which is also framed by the same angles of the tower shapes, feels both grand and humanly scaled, and functions a bit like the narthex of a cathedral. Traditionally, the narthex was an entrance space facing west (like the west front of Pei’s National Gallery building), and in early Christian churches, and still in some later ones, it often felt a little constrained, with a lower ceiling, to accentuate the drama of entering the main body of the religious space.

And that is absolutely how the entrance to the East Building works. You pass under a kind of bridge above the entrance and enter into the vast, open, sun-drenched interior. If you visit the East Building after spending time in the West Building, where the galleries are mostly without windows and natural light is contained mainly in the corridors, the volume of open space in the East Building feels celestial.

Pei’s solution to the spatial challenges of the building’s site was a simple, brilliant geometrical insight: He forged two triangles, one with two equal sides (the isosceles triangle that contains the public galleries and atrium) and a right triangle (which houses the gallery’s library and offices). In an early 1968 drawing, made with red crayon and pencil, you see the flash of discovery, the fusion of the two triangles and a bold red arrow pointing into the Fourth Street face of the building, continuing the energy from the West Building into the new space.

You also see Pei dividing up these big triangles into a few smaller ones. Later drawings would continue that pattern almost obsessively, until the whole building had been worked out into something like a fractal form, a complex, interlocking grid of triangular forms. Those lines are still visible throughout the building, in the shape of the smaller spaces, in the towers, in the flooring and in the patterns of the skylight, which was an engineering marvel at the time. These repetitions are subtle, but insistent, and they give Pei’s modernism a quiet intentionality throughout all its parts. Nothing in this building feels accidental, or provisional.

Of course, the place you see the triangular form with greatest drama is along Fourth Street, where the right-angled volume of the office-and-library triangle comes to a sharp point, now rubbed with public affection into a shiny knife’s edge. This is another marvel of the space: a modernist building that has become tactile, something that people touch and revere. Pei worked within an idiom that produced some impressive buildings, admirable spaces, clean, functional forms that got the job done. But with this little haptic detail, he created something that visitors also found miraculous, even perhaps a bit superstitious, something that could be touched like the foot of a statue that is said to have powers of healing or good luck.

There were complaints and criticism at the time. The East Building devotes much of its space to its atrium, with the galleries pushed to the sides. Isn’t that a waste of space? Should so much volume be left simply empty, except for the light and the low din of crowds passing through?

In 2006, the National Gallery filled the atrium with 16 grand pianos and a battery of percussion instruments, linked to a computer that was programmed to play a 1926 piece by George Antheil called “Le Ballet Mécanique.” It was a noisy, raucous, clangorous affair, and when the piece was playing, people emerged from the galleries and listened in wonder to the noise bouncing off every surface of Pei’s giant atrium. It made manifest in a clear and vibrant way the mostly hidden logic of the National Gallery, which is that all paths lead to Pei’s building, and it never fails to delight when you get there.