If there seems something a little incongruous in the 50-year friendship between Isamu Noguchi and Buckminster Fuller, that is probably because it is hard to imagine what could be considered standard in any friendship of which Fuller was one half: This myriad-minded polymath was as live a wire as anyone had ever seen.

This incongruity, however, does not result from the fact that the great Japanese-American sculptor was an artist while Fuller was a man of science, an inventor, and an architect. Rather, as a new exhibition at the Noguchi Center suggests, both men had powerful imaginations, and it seems likely that Fuller was the bigger mooncalf of the two.

Given its venue, this show is really about Noguchi and the improbable influence that Fuller, nine years his senior, had on him. It is difficult to see much influence flowing in the other direction. Nevertheless, this exhibition proves that there was considerable interpenetration of their respective domains. Fuller – or at least his workshop – produced at least three admirable sculptures that are on view at the Noguchi Museum, while Noguchi himself proved to be a skilled architect in a Fulleresque idiom.

Born in 1895 to an illustrious family of Boston Brahmans, Fuller was twice expelled from Harvard and never earned a degree. Thereafter, he decided to dedicate his long life to improving an imperfect world through his prolific writings and his designs for streamlined living. In time he tackled everything from the physics of subatomic particles to the aerodynamics of cars (a scale model is on view in this show) and the streamlining of model homes.

This unrelenting propeller head loved new linguistic coinages like “tensegrity,” apparently a combination of tensile and integrity, and “Dymaxion,” a combination of dynamic, maximal, and something else. Along with the crystal and pyramid enthusiasts of a later date, he had an implicit faith in the power of combined tetrahedrons – like those seen at the entrance of the exhibit – to foster human happiness.

Noguchi was born in 1904 to a Japanese father and an American mother. He spent much of his equally long life shuttling from America to Japan, from Italy to France. He apparently spoke English with a slight Japanese accent and Japanese with a strong American accent.

The two men met in 1929 at a oncefamous bohemian dive in the West Village known as Romany Marie’s, and their friendship remained in force until Fuller’s death in 1981.

One of the earliest works in the show is Noguchi’s chrome-plated bronze head of Fuller. Although Noguchi was destined to become one of America’s greatest sculptors, his earliest efforts were startlingly hesitant and conventional. This highly schematic head, for example, reduced Fuller to a few sharp planes that suggest the sort of overblown Nietzschean superman that meant far more back then than it does today.There is also some distant formal continuity between this piece and the works of Brancusi, with whom Noguchi studied in Paris.

After meeting Fuller, the artist developed a far greater interest in constructed objects. Consider two very different works that Noguchi created in 1943: “Bucky,” an abstract configuration made out of wire and wood, and “House of Heroes,” a totem pole of sorts, fashioned from wood, paper, bone, and string. Both derive partially from the sort of engineering that Fuller developed, but it is difficult to credit Fuller as their principal inspiration. Rather, Noguchi was responding to two powerful impulses – unacknowledged by the show – that were alive in early modernist sculpture: the Constructivism of the Russian avant-garde, as evident in Naum Gabo and Antoine Pevsner, and the early Surrealism of Alberto Giacometti and the collateral influence of Alexander Calder.

In fact, it was Surrealism in one form or another that was to have the greatest influence on Noguchi’s sculpture. His intuitive response to the sensual suggestiveness of elements like flowing water and stone, whether rough-hewn or burnished into biomorphic abstractions, is essential to most of his subsequent career.

Such are the works most often associated with the sculptor. But there was another side of him that could resurface at any time – as befitted his ad hoc and pluralistic creativity. Rigorously geometric, this aspect of his style was more often applied to architectural projects than to sculpture, and it does betray, often explicitly, the influence of Fuller.

An excellent example is the monument that NASA commissioned from him to commemorate the Challenger astronauts: Its 35- foot concatenation of tetrahedrons specifically refers to the “Tensegrity Mast”that Fuller designed for MoMA in 1959. Another clear debt to Fuller is Noguchi’s design – unfortunately never realized – for a Martha Graham Dance Theatre in 1988.

One of the surprises of the exhibition is that Fuller’s studio could itself produce some lovely sculptures, as is evident in “90 Strut Tensegrity,” a diaphanous mirage of a balancing act fashioned from wire and chrome-plated metal. Ironically, this and two similar works from the late 1970s reveal the influence of Calder and the Russian avant-garde, but little of Noguchi.

Until October 15 (9-01 33rd Road, at Vernon Boulevard, Queens, 718-204-7088).