This story has three sides (it’s about flatiron buildings)

Every traveler has weaknesses. With my wife, it’s horses and shoe stores. Mine – well, one of mine -- is flatiron buildings.

Put me in front of a three-sided building – tall, squat, immaculate or broken down -- and my jaw goes slack. Pretty soon my camera’s memory is full and I’m circling the property, trying doorknobs. My name is Reynolds and if I’m getting the Latin right, I am a trivallumophile.

The telltale moment came early this year, on a trip to Arizona. There I sat in Jerome, an old mining town that looks to be slowly sliding down a hardscabble hillside between Sedona and Flagstaff. I was done with breakfast and due to be on the road, but something was keeping me. What?

The restaurant. It was a tiny buliding, but it had three sides, with a big window looking out upon Jerome’s least sleepy intersection. Flatiron Café, said the letters painted in gold on that window. The morning sun was bouncing all over, there was a room for rent upstairs, and I didn’t want to leave.

There’s no great mystery to flatiron buildings. Most of the North American specimens rose between 1890 and 1920, when cities started sprouting skyscrapers.

Often, a flatiron marks the spot where one neighborhood’s street grid inelegantly meets another. Sometimes it’s other factors that produce an irregularly shaped lot. However the odd lot is created, developers are bound to look for ways to maximize space. And then they press architects to strut their ingenuity. Sometimes, you get gorgeous results.

And frequently you can can eat, drink or sleep in those results. Here are five North American flatirons I’ve seen up close and enjoyed (beginning with that café in Jerome), followed by five I’d like to see -- although in the last case, I’d be happy to admire it from across the street.

In Jerome: Flatiron Café, 416 Main St., Jerome; (928) 634-2733. Apparently built in 1913. Two stories, with space downstairs for just three tables, a handful of guests and two employees in the dining room. You can rent the upstairs room, which is called “The Flat” and fetches $200 nightly, two meals included, two-person maximum, no children.

In New York: The Flatiron Building (a.k.a. Fuller Building), 175 Fifth Ave. Bordered by Broadway and East 22^nd Street, neighbored by the greenery of Madison Square Park. Built in 1902, home to offices, about 285 feet tall. More info here.

In Denver: Brown Palace Hotel, 321 17^th St.. Opened 1892. Housed the Beatles in 1964 and many presidents before and after that. Tours at 3 p.m. Wednesdays and Saturdays at 3 p.m., $10 a person. Overnight guests pay $164 nightly and up.

In San Francisco: Columbus Tower (a.k.a. the Sentinel Building), 916 Kearny St. Its green hue and location along Columbus Avenue puts it into dramatic contrast with the taller, newer, paler Transamerica Pyramid, a few blocks southeast. Completed in 1907 and sited in North Beach, the Columbus Tower is now headquarters to Francis Coppola’s American Zoetrope production company, and the ground floor is home to the Café Zoetrope, (415) 291-1700.

In Portland, Ore.: Ringlers Annex, 1223 S.W. Stark. Built in 1917 in the West Burnside area. Neighbored by McMenamin’s Crystal Hotel and Zeus Café, this building is described by its operators as a “pint-sized pub,” with a main floor, mezzanine and basement bar.

In Chicago: Flatiron Arts Building, 1579 N. Milwaukee Ave.. Home to many art studios. Sited in the Wicker Park/Bucktown area.

In Atlanta: English-American Building, a.k.a. the Flatiron Building, 84 Peachtree St.. Built in 1897, 11 stories, bordered by Broad and Poplar streets in downtown Atlanta. More info here.

In Toronto: Gooderham Building, 49 Wellington St., East, Toronto, on the east edge of the financial district. Completed in 1892. Five stories. Red bricks, a jaunty capped turret, and a pub in the basement: Flatiron & Firkin (416) 362-3444.

In Los Angeles County, the Culver Hotel, 9400 Culver Blvd., Culver City; (310) 558-9400. Six stories, opened in 1924, idle for decades, now a hotel again with 46 rooms. It might not be as tall and slim as some others here, but John Wayne once owned it, and guests in the old days included scores of actors who portrayed munchkins in the 1938 filming of “The Wizard of Oz” at nearby MGM studios. Most rooms usually $229-$289. Most in demand are the four corner units (“flatiron queens”), which feature windows looking three directions.

Meanwhile, in Vancouver, Canada, that British Columbian city’s Gastown area has many flatiron buildings (here is an explanation with examples) including the six-story Hotel Europe Building, 43 Powell St., Vancouver. In exterior photos it looks great. But the building, now operated as rental residences by an affordable-housing venture, gets alarming ink here. Maybe I’ll just admire it from outside.