Traditionally, for obvious reasons, buildings are either a uniform width or taper inward as they go up.
Are there any buildings that are the opposite, that are narrower at the base than they are at (or towards) the top?
Also, the Geisel Library Building at UC San Diego, named, of course, for Dr Seuss.
There are a number of house designs that are roughly mushroom shaped. One rather famous one stands in the canyon along I-70 just west of Denver, and was featured in Woody Allen’s “Sleeper”.
These are good for landscapes where it is desired to minimize the footprint while providing adequate living space. A steep rocky hillside would require lots of blasting or drilling to make a level spot to put a ranch style house. By cantilevering off of a smaller stem, a lot of prep work can be saved. It may also be desired to save as much of the natural landscape as possible for aesthetic reasons…or maybe the owner just likes the oddball look.
Well, once you get into cantilevers, all sorts of things are possible. For an extreme example, look at the Institute of Contemporary Art in Boston
Virtually all air traffic control towers would meet this criteria.
This would qualify though it’s not finished yet.
http://londonoffices.com/news/wp-content/uploads/2010/09/walktalk.jpg
It’s what they are calling the walkie talkie in London.
Traditional timber medieval buildings also used to have upper floor bigger than their lowers. Not the best picture but you get the idea.
The CIT Building near Dulles Airport (Virginia suburb of D.C.). Folks around here just call it the “upside-down building.”
Newcastle City Council (Australia) has a more substantial building,
that isn’t a 3 floor artwork (easier to do when its only a few floors), but isn’t sky scraper (just because that category has been covered by the London Walkie Talkie 
)
Its called “The Wedding Cake”.
My parent’s house is like that. It’s several hundred years old, nobody knows exactly how old because the records were destroyed. The idea was that they bought the land and then built out, so it cost less, if that makes sense. Over time, the building has sagged so now it’s completely crooked. It looks a little distressing to see now, but it was intentionally built that way. Upstairs is a little bit bigger than downstairs. I’ll snap a picture next time I’m there.
Unlucky for our neighbours, whose houses were built much later. Their adjoining walls, one on each side, lean in.
Most water towers fit the bill as well, at least here in Finland.
The Hartford Insurance building in Woodbury MN does that. That image however is a bit of an optical illusion as it doesn’t really show that the reverse stepped building has each level more cantilevered over the lower one.
University Hall at UIC.
Rainier Square in downtown Seattle.
Dallas City Hall and it’s digitally-enhanced version from Robocop.
Also the Seattle Public Library counts. Well… I think it does… it kind of folds all over itself.
And of course this thing in Seattle counts as well… well pretty sure, looking at the photo it looks like the diameter of the top is identical to the diameter at the base, so maybe it doesn’t.
There are reasons for the narrower-at-the-top design of tall buildings that have nothing to do with physics, architecture, or engineering limitations. In New York, for example, buildings are required by law to have setbacks every dozen floors or so.
I’m sure the psychology wise dopers can explain some of the others.
The Classen in OKC sort of sits on a pedestal, but it’s technically narrower at the base.
Could just be the photo, but that building is some kind of ugly.