Rice chemistry professor Robert F. Curl Jr. and others noticed surprise readings on the spectrometer: evidence of 60 carbon atoms bonding together, possibly in a hollow cluster shaped something like a soccer ball. Dr. Curl painstakingly went through the results.

It all checked out, Dr. Curl concluded. Suddenly, new frontiers in physical chemistry and nanotechnology were thrown open. They named the discovery after the geodesic domes (think Epcot) of architect and futurist R. Buckminster Fuller: buckminsterfullerenes, or buckyballs for short.

Dr. Curl and two colleagues, Richard Smalley from Rice and Harry Kroto from England’s University of Sussex, shared the Nobel Prize in chemistry in 1996. And buckyballs became famed as a kind of Swiss Army knife of the molecular realm — with potential applications ranging from vessels for hydrogen fuel storage to paint-on solar panels to ultra-strong armor. It was also adopted as the name of a magnetic office toy.

Dr. Curl died July 3 in Houston at age 88 after a six-decade career at Rice, the university said in a statement. No cause was given.

“Bob was our insurance policy,” said James Heath, president of the Institute for Systems Biology in Seattle and one of the graduate students involved in the 1985 experiments. “We were all excited, but he checked every detail before we could announce anything. He made sure what looked interesting was not actually boring.”

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Robert Floyd Curl Jr. was born in Alice, Tex., on Aug. 23, 1933, son of a Methodist minister whose job took the family hopscotching around Texas. His father also helped establish Methodist Hospital in San Antonio.

When Mr. Curl was 9, his parents bought him a chemistry set for Christmas. “Within a week, I had decided to become a chemist,” he wrote in an autobiographic sketch for the Nobel Foundation.

There were no chemistry classes at his elementary school in Texas. He dabbled on his own, making things that sizzled, oozed and exploded. One of his high school teachers gave him special science projects to keep up with his expanding interests.

After graduating in 1954 from what was then Rice Institute, he received a doctorate in chemistry from the University of California at Berkeley in 1957 and went to Harvard University for postdoctoral work on molecular bonds. He then joined the Rice faculty, eventually chairing the chemistry department. He held the title of professor emeritus following his retirement in 2008, at 74.

As a young assistant professor, Dr. Curl began experiments on semiconductors using a laser-and-vacuum apparatus in Smalley’s lab. Dr. Curl then suggested his friend Kroto come from Britain to use the lab for his work, attempting to re-create unusual carbon chains identified by radio astronomy in interstellar clouds and red giants, old stars with relatively low surface temperatures.

That’s how “we got into the carbon business,” Dr. Curl recalled in a 2016 Rice News interview.

The concept of carbon arranging itself in molecular structures, such as spheres or tubes, had been part of scientific inquiry and theories for decades. It wasn’t proved until the unexpected findings from the Rice experiments. The initial work was published in Nature in a manuscript, “C60 Buckminsterfullerene.” (C60 refers to the 60 carbon atoms arrayed in 12 pentagons and 20 hexagons.)

At the time, carbon was thought to exist in just three forms: soot or coal, graphite and diamond.

“No one had ever heard of round carbon before,” Heath said.

It also laid set a new course for nanotechnology, making innovative materials and devices at a near-atomic scale. The strength and stability of buckyballs — in 60-atom form and bigger — has offered dozens of possible uses because of their shape and electron-bonding properties.

Buckyballs have found applications in ultrasmall light-emitting diodes and solar cells. Other research moves in many directions: medical uses such as antioxidants by siphoning up free radicals; mixing with polymers for a possible paint that collects solar power and generates electricity; as potential lubricants because of their round shape, or in ultrathin protective coatings nearly as hard as diamonds.

The buckyball discovery also was key in the development of nanotubes, essentially graphite rolled into atomic-level cylinders, used as super-efficient pathways for electricity and thermal exchange.

Since 1985, buckyball-shaped carbon molecules have been found in nature in some ancient geological formations, possibly delivered by meteors, and in sooty flames. “Think of this the next time you light a candle,” said the presentation speech for the Nobel Prize by Lennart Eberson of the Royal Swedish Academy of Sciences.

These silk worms got a nanotube diet. They produced super silk.

In 2015, Rice named the Smalley-Curl Institute in honor of the two Nobel laureates. Of his fellow Nobel winners, Smalley died 2005 and Kroto in 2016.

In recent years, Dr. Curl worked with Rice economists to study subjects such as energy use and how automation impacted the U.S. economy.

Survivors include his wife of 66 years, the former Jonel Whipple of Houston; two sons, Michael Curl of Houston and David Curl of Fort Worth; and three grandchildren.

“Reporters asked us, ‘Tell us how you made this great discovery,’ ” Dr. Curl told the Houston Chronicle in 2008. “Well, it was a stroke of luck. The only credit you can claim is not ignoring your stroke of luck.”