There is a Star Trek: Voyager episode that shows and interesting arcology skyscraper.
http://memory-alpha.org/en/wiki/Millennium_Gate
It is one kilometer tall and located in the town of Portage Creek, Indiana which doesnt exist but there is a Portage, Indiana that is a northwest Indiana suburb of Chicago. In the episode the downtown of the town was demolished to built it but given that in the ariel picture it appears to be in the middle of cornfields and not on the shores of Lake Michigan and more developed like the real Portage, IN. Its interesting to think of it being near Chicago though, it even has dual spires/antennas just like the John Hancock Center and Sears Tower. Not much is said about it besides its one kilometer height and the fact that its supposed to be a self-contained biosphere, a self contained city or archology. It was also said to be 3.2 kilometers wide at its base but looking at the picture the "biosphere" section doesnt appear to be 3.2 times as wide as the tower is tall, to me it looks only one kilometer wide or the same as the tower's height, so maybe someone else cares to scale it. It was supposed to have broken ground in 2001 and completed in 2012, giving Chicagoland a rival of Burj Dubai
.
I think it would be a very cool idea if someone diagramed it given all the super tall visionary skyscrapers a kilometer in height and higher in the diagrams page. I know its a building from fiction but we have other fictional buildings like the Glass Tower from the Towering Inferno and buildings from Lord of the Rings. Its not a bad looking skyscraper either.