Alexander Calder (1898–1976), a poet with pliers and cutting torch, is one of the greatest and most innovative of modern sculptors.Trained as an engineer and inspired to work abstractly after a visit to Mondrian’s studio in 1930, Calder created strange sculptural hybrids made of equal parts industry, fantasy, Neoplasticism, and nature. His stationary stabiles and moving mobiles — mythic steel creatures related as much to skyscrapers and airplanes as they are to animals and trees — are truly modern and abstract. Yet, seemingly alive, as if materials from a construction site had become magically possessed, Calder’s sculptures leap and frolic like children let out for recess.

New Yorkers can readily see Calder’s large outdoor sculptures throughout the city in places as diverse as Avery Fisher Hall at Lincoln Center, Seagram Plaza, and John F. Kennedy International Airport’s Terminal 4. “Cirque Calder” (1926–30), currently on view at the Whitney Museum of American Art, provides us with yet another side of the artist. However, getting a true grasp of the virtuosity, breadth, and ingenuity of Calder’s oeuvre requires seeing a number of his works in quick succession. This rare opportunity is currently available in a small yet enthralling exhibition of six sculptures, “Alexander Calder in New York,” that is up through March in Manhattan’s City Hall and City Hall Park.

More than any other artist, Calder successfully transformed art-making into child’s play. Organized by the Public Art Fund, this gathering of works that resemble flora, fauna, gargantuan toys, and jungle gyms will appeal to the child in everyone.

Calder’s ease, grace, and virtuosity with his materials make his sculptures look effortless. (Maybe they were.) When Calder was asked to exhibit his work at Harvard University in 1930, undergraduates Lincoln Kirstein and Edward Warburg met the artist at the airport a couple of hours before the exhibition was scheduled to open. “Where are the sculptures?” they nervously asked. Calder showed them a pair of pliers and a spool of wire. During the car ride to the university, he began creating wire portraits of his travel companions. By the time the show opened, Calder had filled the gallery with sculptures.

Playfulness, of course, whether it is suffused or at center stage, is only one element of a work of art. Calder may attract us with brightly colored shapes and anthropomorphic forms, and he may continue to hold us with his wit and jocularity; but after we have been pulled into the dance, we stay because of the artist’s seriousness — a seriousness that, regardless of the his subject matter, shows that Calder explored his chosen metaphors fully and beautifully.

The exhibition can be seen in full only if you sign up for a free tour (City Hall is off-limits to the general public, a peculiar if not contradictory requirement for a show sponsored by the Public Art Fund). I strongly recommend that viewers take the tour, since it is only then that they have the chance to see the spectacular mobile “Untitled” (1976), which hangs from the center of the sky-lit dome in the City Hall Rotunda. The only mobile in the exhibition, “Untitled” is a black counter to the white “Ghost,” which hangs above the steps in the entrance of the Philadelphia Museum of Art. Made up of five planar forms suspended on four rods and a central wire, “Untitled” drifts gorgeously in its neoclassical setting as if it were a giant hovering insect taking in its foreign surroundings. And yet, after spending time with the sculpture, it becomes apparent that the surroundings are not that foreign after all.

The leaflike forms play against the clear geometry of the rotunda. One of the black shapes looks like the blade of a weapon or a swollen boomerang; another is shaped like a tear; another rounder form looks like a gibbous moon. The forms’ shifts out of pure geometry play against the exactitude of the dome, the marble stairway, and the Corinthian columns.As the mobile floats in the space, it changes character. At one point, the sculpture threatens menacingly like helicopter blades or a giant bird of prey. Then it spreads outward into a creature that, with its childlike head, wings, and heavy feet, feels like a fledgling gaining altitude.

Outside, all but one of the sculptures is behind a fence. “Jerusalem Stabile (1:3 Intermediate Marquette)” (1976) is the only work that can be walked around entirely. The other works feel like animals in cages in a zoo.This may add to the anthropomorphic experience of the sculptures, but in the end this works against them. The inability to walk around Calder’s sculptures, which can change considerably within a distance of only a few inches, robs the works of their full power. Still, without complete access to the sculptures, much can be seen simply by walking the paths and sidewalks around City Hall Park.

No matter how much access you are granted to a Calder sculpture, the work can still be elusive. “Seven-Legged Beast” (1957), like most of the sculptures, can be seen only from a couple of viewpoints and through the fence. Still, it has a lot to offer. The black steel sculpture is goofy and graceful. It has the lightness of a ballerina, the thrust of a pack of racehorses, and the gawkiness of an adolescent. Made up of six planes that seem to unfold in succession like a Futurist sculpture or an accordion, “Seven-Legged Beast” leaps upward like dolphins, fans outward like a butterfly, and extends its legs like can-can dancers.

“Le Chien en Trois Couleurs (Three-Colored Dog)” (1973), like origami, is angular and folded. Comprising numerous intersecting triangles, the red, black, and blue sculpture explores the full range of its subject. The triangles become ears, snout, mouth, and incisors. Seen from one end the sculpture looks like a dog, its open mouth sniffing the air, sitting on its haunches. From another angle, a triangle, like a leg, seems to be lifted, as if the “Dog” were marking his territory.

Moving around Calder’s sculptures, points become lines, which become planes, which revert back to points. Seen from the side “The Cock’s Comb” (1960) is feathery, jovial, and cocky. Lithe, strutting, and curly, it looks like a black crown, and it appears to prance and peck. Its forms suggest beak, comb, and wattle. From another viewpoint a little farther down the sidewalk, the sculpture’s pointed peaks gather together, lean, and lick the wind like flames.

In this exhibition, all of Calder’s sculptures, seen framed among, or framing, the buildings and the trees, feel equally at home in both the city and the country.”The Arches” (1959), a black, daddy longlegs–like sculpture made up of high-stepping arches, benefits greatly among the trees. The sculpture appears to bow and sway like branches or sails, and to feel rooted to the earth. Seen from a distance through the trees, its planes are the same size and shape as nearby leaves. Its arches and flying buttresses suggest those found in cathedrals, and from another viewpoint its silhouette — with its two spires, one taller than the other — is reminiscent of Chartres Cathedral.

Still, one of the greatest experiences in the exhibition is that of “Jerusalem Stabile (1:3 Intermediate Maquette)” (1976). A bright orange 24-foot-long series of arches, legs, and a pointed tail, it is the largest work on view, and it sits on the wide sidewalk east of City Hall Park at the base of the Brooklyn Bridge. A maquette of the original, which is in Jerusalem, “Jerusalem Stabile” is a horizontal sculpture made up of openings, bridges, mountains, and planes that suggest both the Wailing Wall and the City of Gates.

The perfect placement of “Jerusalem Stabile” rivals that of any outdoor sculpture in New York. Seen from one side (looking west), its arches frame City Hall Park, the main gate, and City Hall itself; seen from the other side (looking east), the Brooklyn Bridge, with its Gothic arches, is framed within the sculpture’s central arch; and seen from its tail end, the sculpture becomes a living, huddled mass. “Jerusalem Stabile,” a wall become gate become portal, bridges industry and nature, city and park, Brooklyn and Manhattan, New World and Old.

Until March 18 (City Hall Rotunda and City Hall Park, between Broadway, Park Row, Chambers, and Center streets, 212-NEW-YORK).