I had assumed the Flatiron building was unique. Ran across this crime story and thought the building was the Flatiron. But a quick Google reminded me the real one has many more floors and is in limestone. The Flatiron is one of my favorite designs. I spent a full hour enjoying all the details in these photos. I can only imagine the lucky people working there. Especially the offices in the tip with windows on three sides.
How commonly did triangular shaped buildings get built?
San Francisco has a few… most notable being Columbus Tower:
Very nice building. Theres just something about this shape that makes these buildings attractive.
Well, this here building in Toronto predates it by about a decade, so maybe the question should be “Did the Gooderham Building get copied elsewhere and in NY”! 
I am sure there are dozens if not hundreds of triangular buildings in New York alone, anywhere streets meet at odd angles. Another famous one is occupied by Delmonico’s restaurant on South William St. in lower Manhattan.
Here’s a more modest but similar building in Belfast.
Prior to 1920 or so, there were essentially no restrictions on the size and shape of skyscrapers - it could be whatever shape you wanted, fill in as much of the lot as you wanted, and be as tall as you could afford. They had a triangular lot at the meeting of 5th and Broadway, so they built a triangular building. Simple as that.
Later on, they changed the building code, mandating setbacks from the street and other architectural restrictions, which led to the famous New York skyscraper look a la the Empire State Building.
Cleveland has one. It was built in 1897.
I see your Gooderham and offer up the 1885 Occidental Hotel in Seattle. It too was triangular until it burned in the 1889 Seattle Fire. Replaced in 1890 by the triangular Seattle Hotel and then in 1961 by the “Sinking Ship” garage.
Chicago has the Northwest Tower or “Coyote Building” at a similar six-corners intersection. There are various wedge-shaped buildings on Chicago’s diagonal main streets (Milwaukee Ave., Lincoln Ave., etc.) but that’s the most prominent.
I had no idea that shape of building was so common. I learned something today. 
I’m glad I asked the question here. I knew you guys would know the straight dope.
According to wikipedia, there are a lot of them. A few of which pre-date the one in New York.
It just depends on how the streets are laid out - if they tend to come to points the buildings will too.
Though not as tall as the Flatiron building due to height restrictions, you see LOTS of buildings-coming-to-a-triangular-point in Paris, for example - pan around just this one intersection and you’ll see a few.
Until this thread I had no idea that “flatiron” was a geologic term and that the building was named after the geologic feature.
The Cathedral Building in Oakland, CA is similar to the Flatiron Building.
The perspective on that photo is really strange. Look at the building on the left, see how it leans over. I’m not convinced that building is triangular at all, at least not a particularly sharp angle.
Both the building and the geological feature are named after cast-iron flatirons, which were more or less triangular.
It’s at least a medium-sharp point, being the building at the East corner of Broadway and W. 211th Street, here.
I know what you mean, though, with respect to the distortion that wide-angle lenses can create.
[URL=“Google Maps”]
There are hundreds of modern corporate buildings built that way for essentially aesthetic, rather than lot-space-filling, reasons.
For awhile my small 20-person outfit rented one section of a 3-story 1980s construction building with a very prominent ship’s prow-shaped end. It was in a corporate park of many similar buildings and pointed menacingly towards a nearby freeway. This was in greater St. Louis, MO.
Ref the OP’s statement that the narrow corner offices were good …
For awhile I had our prow-office. it was a PITA since there was a lot of floor space that was a useless shape; no furniture could go there. So despite a huge square footage it was actually a small office usability-wise.
As well it was all surface area. There was one interior wall about 15 feet wide which included a door into the rest of our office space plus two exterior walls each 25 feet wide that met at a point, the prow of the building. Those walls were all windows. One faced more or less East and the other West. Which meant the whole office baked in the summer & froze in the winter.
A conventional 90 degree corner office was *much *nicer.
That’s not a flatiron-type building. It’s oddly-shaped, but it’s not a narrow triangle.
[URL=“Google Maps”]Here’s the actual Flatiron Building](Google Maps) seen from above.
