Since its founding nearly 80 years ago, the Museum of Modern Art has placed Picasso at the center of its narrative of Modernism, and supported this viewpoint with impressive exhibitions of his work and a superb collection of his paintings. Less familiar to many museumgoers is his sculpture, a medium to which he periodically returned during his long career, but only occasionally exhibited. The first comprehensive show of these works took place when the artist was in his mid-80s, and this facet of his lifework is the subject of the latest of the “Focus” installations highlighting portions of the museum’s collections.

Installed unfussily in a single fourth-floor gallery, the 12 sculptures spanning five decades make for a small but ravishing show. Their variety, inventiveness, and force present the full breadth of Picasso’s genius, and hint intriguingly at the way that his plastic experiments migrated between sculpture and painting.

The earliest piece in the installation is a bronze head from 1909 of his mistress Fernande Olivier. Deep, almost savage furrowings of the face and hair convey interior dimensions with wondrous vigor. As with much of the artist’s work, a strategic asymmetry — one side of the jaw protruding, in this case, with lips tugging the other way, and the opposite eye socket protruding — initiates a leapfrogging of points that vitalizes the masses within. (Visitors can view on the fifth floor the two-dimensional counterpart of this piece, painted by Picasso shortly before; the “Woman with Pears” from the same year shows his painting evolving toward the low-relief, multifaceted style of Analytic Cubism.)

In a nearby display case, a real spoon adorns the top of the diminutive bronze sculpture “Glass of Absinthe” (1914). Its shiny horizontal note of metal neatly finishes off the column of swirling planes that shape the glass, connecting its interior with the surrounding air. The integration of the spoon into the sculpture represents, of course, a three-dimensional version of the collage technique pioneered by Picasso and Braque two years earlier. Endlessly inventive, the artist has further mixed his media by painting a polka-dot texture on both the surface of the liquor and a sugar cube perched on the spoon.

The most historically significant work might be overlooked by some museumgoers. Hung high up on an opposite wall, an unassuming assemblage of wire and sheet metal titled “Guitar” (after 1914) exemplifies the constructed sculptures that mark Picasso’s radical break from traditionally carved and modeled objects. This piece — actually a more durable version of a cardboard maquette from 1912 — set the precedent for an entire idiom of modern sculpture based on assembled geometric units. Though a uniformly dull brown, the rhythms of its fragmentary interior and outer planes palpably mold the instrument’s complex volumes. “Guitar” achieves what any great sculpture does — vivid articulations of mass through surface tensions — but here Picasso has drastically distilled the process to the humblest forms and materials.

The artist’s modeling is even more reductive in the 6 1/2-foot-tall “Project for a Monument to Guillaume Apollinaire,” a welded-rod sculpture constructed in 1962 from a 1928 maquette. (A still larger version resides in the center of the museum’s sculpture garden.) In this “drawing in air,” the wrapping planes of “Guitar” give way to straight and arcing steel rods that seem to endlessly circulate and redefine a discrete space. A small disc presiding at the top reads inevitably as a face, despite the lack of anything approximating human limbs or extremities.

Vastly different again is “Head of a Woman” (1932), a plaster sculpture produced four years after the original design for the Apollinaire project. Its bulky, brutal swellings capture a likeness of Picasso’s young mistress Marie-Thérèse Walter at several times the natural size. Somehow, the grotesquely muscular forms convey the most delicate of expressions: the subject’s shy hesitance. In the far smaller “Head” (1958), the artist revisits the spare geometry of his early Cubist constructions, turning the void of an empty wooden box into the substantial impression of a face; its broad volume gathers poignantly into the beady button-eyes tacked to the single slat of a nose.

In this selection of work, Picasso repeatedly gets away with devices that would seem mere gimmicks in lesser hands. The incorporated tree branches and textures of myriad nailheads, for instance, feel natural, even necessary, to the tensile vigor of the plywood “Bull” (c. 1958), in which slender, elegant legs support the broad arabesques of haunches and head. To be sure, an element of habit sneaks into the virtuosity of some of the later pieces. One senses that the artist had lost all anxiety about his legacy by the time he fashioned the 1951 bronze “Goat Skull and Bottle,” which seems little more than the sum of its parts. The bronze “Baboon and Young” (1951), with its toy-car face, cup-handle ears, and car-spring tail, wrings a little too much mileage out of a delightful conceit. At this point the artist seems all too comfortable with the aura of master-at-play.

As Picasso claimed, his goal was not to seek but to find, and his sculptures are most moving ultimately for their discoveries, not of stylistic mannerisms, but of his subjects’ deeper characters. In these works, a seemingly offhand gesture — such as the small, incised eyes among the swelling mounds of Marie-Thérèse’s head — becomes a culmination. A fanciful flourish — the framing of the bull’s face with real stretcher bars — draws us inexorably to the identifying moment. Arguably, the exhibition might have benefited from the inclusion of one or two related paintings, to highlight the traversals between two and three dimensions. But the understated installation admirably allows the artist’s achievement to speak for itself. The investigations of countless younger sculptors, as diverse as David Smith and Henry Moore, can be traced to the works in this gallery. “Focus: Picasso Sculpture” reminds us that in the coherence and force of Picasso’s perceptions, and the fluency and variety of their formal expression, he remains unsurpassed.

Until November 3 (11 W. 53rd St., between Fifth and Sixth avenues, 212-708-9400).