Old streets in cities were sometimes at odd angles. This resulted in someone squeezing a building in to the available space. New Year is most famous with the Flatiron Building which appeared here. Oakland also had a building which I covered here. Vancouver has a similar building. I guess, if your city is of a certain vintage, you may well have something similar.
I saw something online about people building houses in unusual spaces. Sometimes this was because that was all the space that they had available. Other times they did it to spite someone who had the adjacent property. One of them turned out to be in Seattle so I decided to check it out when we were over there running some other errands. It is located in Montlake.
The house is a wedge shape. If you look at it from the main road, it looks like a relatively normal frontage. Nothing too special. From the wide end, it seems like a single room width property. There is a garage underneath and rooms above. Go to the other end, though, and you see just how much it narrows down. There is space for a door and that is about it. A trip to Google Maps will show you the footprint of the house and you can see how it has been squeezed in. A weird place for sure but apparently a popular house to own judging by the price it has sold for in the past!
New York has many iconic buildings. One of the more famous buildings is the Flatiron Building. At the narrow intersection of two streets, it makes use of the space available. New York is not alone in having such intersections so it is not alone with buildings to fill the (limited) available space. Oakland has a similar spot where Telegraph splits off from Broadway. The building that sits there is so thin it is actually quite hard to show that it is a building rather than just a tower!
The city has just gone through a rebuild program to create a public space in front of the building and the area is now more accessible than it used to be. From the statue in front the sides of the building can disappear, so thin it is. At the moment the first floor of the building is vacant and available for lease. I did find myself wondering what I could do with such a space but it does look pretty impractical. I imagine that is why it is still empty.