Lawrence Mauro is used to strangers gawking at the eight-sided 1860 house he owns in Stockport, N.Y. And for the most part, he’s fine with it. But one day a few years ago, the curiosity got out of hand.

“I had dislocated a disc,” he said, recalling that he was in a lot of pain and needed to go to the hospital. “And the two ambulance drivers come in with the gurney, and one of them says, ‘Oh, I’ve always wanted to know what the inside of this house looked like.’ And I said, ‘Not now!’”

The house owned by Mr. Mauro, 62, a retired landscape architect who worked for the New York City Department of Parks and Recreation, and his husband, Bob Pesce, 70, a ceramic artist, is one of nearly 1,500 octagonal homes built in North America during a brief 19th-century fad. The unconventional shape was healthier and made more efficient use of space, their adherents argued.

More than 300 of those houses are still standing, mostly in the Northeast and Midwest, said Ellen L. Peurzer, an historian whose website is a clearinghouse for information about octagonal houses. And in some places, octagons are still being built, thanks to their panoramic views and slight advantage over conventional homes at resisting hurricane-force winds.

But with their odd angles and rooms shaped like slices of pie, they aren’t for everyone. They can be difficult to furnish and repair. And they almost always attract attention.

Their fans wouldn’t have it any other way.

When Roberta Walsh and her husband, Stephen Walsh, first saw the 1849 octagon built by Linus Yale Sr., a lock tycoon, in Newport, N.Y., it was love at first sight. Made of limestone, with a spiral staircase, stone pillars and a cupola, the house looked like a castle, she thought.

“We said, ‘Holy Moly! We are never going to have an opportunity like this ever again in our whole lives. We’ve got to buy this house,’” said Ms. Walsh, now 69, a retired librarian who worked at Ulster County Community College.

Getting inside wasn’t easy. Although the house had been on the market for a while, so many curiosity seekers had asked to tour it that the listing agent had stopped returning calls, she said. But she and Mr. Walsh, now 70, a retired software engineer who worked for IBM, persisted. In 2005, they bought the house for $180,000 and moved to the Herkimer County village from their Hudson Valley home three hours south.

Settling in has been difficult, because of the shape of the rooms. When the couple try to figure out where furniture should go, “we make each other crazy,” Ms. Walsh said. “I’ll line a sofa up on one wall, and then he’ll come in and say, ‘No, no, no, no, no. It’s got to move out this way. You’ve got to pull this end out.’ And I’ll push it back. And he’ll pull it out.”

But what the Walshes regard as a creative challenge was once seen as an advantage — or at least a small price to pay, given the benefits of living in an octagon. Orson S. Fowler, the amateur architect who popularized octagonal buildings in the 19th century, made elaborate claims about their aesthetic superiority and health benefits. (Notably, he was also the country’s foremost proponent of phrenology, the pseudoscience of reading people’s characters by studying the bumps on their heads.)

Buildings were more visually appealing when they were round, like fruit, Mr. Fowler maintained. In his 1848 book, “The Octagon House: A Home for All,” he wrote: “The more acute the angle, the less beautiful; but the more the angle approaches the circle, the more beautiful.”

Because round houses were expensive to build, Mr. Fowler settled on the octagon as the next best thing. With windows on all sides, octagonal homes had more light and better airflow, so they were healthier to live in, he claimed, and they made better use of space. “All the rooms are united, so that you could go from one to another, without being obliged to pass through a cold and cheerless entry,” he wrote.

That sort of floor plan, he explained, would make housework easier — “especially for the weakly woman” — because there would be a shorter distance to traverse from the kitchen to the laundry. As he saw it, there was almost no domestic endeavor that could not be done better in an octagon.

Over the years, many of Mr. Fowler’s claims have been dismissed, but a few have held up.

Joseph Pell Lombardi, an architect who owns and restored the magnificent Armour-Stiner House, in Irvington, N.Y., agrees that the many windows provide prodigious light. “In a square or rectangular house, there are times of day when the sun’s hitting the corner, and there’s less light coming in the house,” Mr. Lombardi, 82, said. “In an octagonal house, as the sun goes around, the different rooms stay in sunshine. That’s just terrific.”

Because many octagonal homes have central staircases that open to the roof, they tend to enjoy good ventilation, making them easier to cool. But that can also be true of more conventionally shaped houses with roof access, Mr. Lombardi noted.

And he is skeptical about Mr. Fowler’s claim that eight-sided houses make better use of space. These houses typically have some square rooms, he said, but because of the exterior shape, many of the leftover spaces are inevitably triangular. In smaller houses, those rooms are often used as pantries and closets; in bigger houses, they become something of a design problem.

“A triangular room is kind of a funny room,” he said. “When you look at it from the door, it looks like a big room. But when you walk into it, you immediately fill it up. So they’re just curious kinds of rooms.”

The unconventional layout, however, is something that fans like Mr. Pesce appreciate.

In a traditional house, he said, it’s fairly obvious what purpose a room is supposed to serve: “‘This is where I do my sewing. This is where I watch TV. This is where I do this.’ I like an openness and a kind of flow. It’s basically my life philosophy.”

In an octagon, the rooms are often grouped around a central staircase, which gives them a more open feeling and allows for a certain amount of design experimentation. What was the living room could become the dining room and then, perhaps, a bedroom. Rooms tend to flow into each other, Mr. Pesce said.

And there’s another feature that he and Mr. Mauro appreciate: The house has a ghost.

In their heyday, octagonal homes were popular with spiritualists who believed that the unusual layout made it difficult for spirits to hide, and therefore easier to contain or capture, Mr. Mauro said. The unmarried sister of the original owner of his house — “Aunt Rachel,” the couple call her — held séances there, he said, and she remains a benevolent presence, although she sometimes interrupts dinner parties and moves the furniture around. (He’s kidding. Sort of.)

By the late 1860s, the octagon craze had begun to wane, perhaps because of the cost: Framing an octagon was more complicated and required more labor than building a conventional house, Mr. Lombardi said.

In the ensuing decades, many octagonal houses were allowed to fall into disrepair and torn down, including Mr. Fowler’s own 60-room home in Fishkill, N.Y., on the Hudson River. Some became schools or public buildings; others were renovated or expanded, altering their geometry.

When octagons are built today, it is usually in resort areas, where the many windows make them popular with vacationers, or in places prone to hurricanes. That’s because octagons tend to have hip roofs that are bolted down on more sides, so they’re less likely to fly off than a typical gable roof, said Anne D. Cope, the chief engineer at the Insurance Institute for Business & Home Safety, an industry group that researches how to protect homes and businesses from severe weather.

The lack of sharp angles can make octagonal buildings a little less vulnerable to strong winds, she said: “On average, something that has a good aerodynamic shape, like an octagonal house, will have slightly — and just slightly — lower wind loads that come down through the walls and into the foundation than a house of the same size in the same spot that is a cube.”

Still, octagonal homes remain something of a niche market, said Jonathan Hallam, a real estate agent with the Kinderhook Group, who once owned Mr. Mauro and Mr. Pesce’s house. When one of them comes on the market, he said, it tends to attract a certain kind of person: “Someone who is passionate about art and architecture, and really wants to live in something unique.”

As he put it, “It’s a rarefied buyer.”

Those who like octagons, however, tend to be devoted to them. Ms. Walsh, for one, has never regretted her decision to buy an octagonal home.

“Every time we pull in the driveway,” she said, “I think the people who live in this house are the luckiest people in the world.”

Looking for Your Own Octagon? There Are Usually a Few on the Market …

Colrain, Mass. | $829,000

This five-bedroom, three-bathroom house is on 9.2 acres in a rural part of western Massachusetts. It was built in 1993, making it one of the newer octagons on the market. The house is relatively big — 6,356 square feet — and has a grand central hallway with a domed ceiling.

Monroeville, Ohio | $199,900

This Italianate brick octagon, built in the mid 19th century by a merchant named John Hosford, is on the main drag of a small village halfway between Cleveland and Toledo, Ohio. It has four bedrooms, two bathrooms, a wooden spiral staircase that rises from the basement to the third floor, a cupola and a veranda that wraps around three sides of the house.

Hamden, N.Y. | $999,000

This 1855 house is on 80 acres straddling a state highway in Delaware County, N.Y. It is being sold as part of Octagon Farm, a complex of buildings that includes a barn, outbuildings and a former cidery with a large owner’s apartment. Built of local quarried stone and later resurfaced with brick, the home has five bedrooms, two and a half bathrooms, a circular staircase and 11-and-a-half-foot ceilings.

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