I couldn't finish this travel log without mentioning the most unusual building I've probably ever seen: Hundertwasserhaus, undoubtedly one of Vienna's most visited sites. It's in the same District as my daughter's apartment, so we see it often. It's hard to take a picture of, but here is one view looking up.
Hundertwasserhaus is the creation of artist Friedenscreich Hundertwasser, a most unusual artist - a painter, sculptor, and architect. He was famous for his bold, unusual paintings, but he is best known for his revolutionary architectural designs. They imaginatively incorporate elements of the landscape and make use of irregular forms. He hardly ever uses straight lines, saying they are "the devil's tools". Just imagine a building with no straight lines!
The first building he designed was Hundertwasserhaus, which is basically public housing and remains so today - so you can only see it from the outside. He charged no fee for its design. It was built between 1983 and 1986, and features undulating floors ("an uneven floor is a divine melody to the feet"), a roof covered with earth and grass, and large trees growing from inside the rooms, with limbs extending from windows. You almost have to see it to believe it - but go to the link that shows Pictures - some are of the inside.
Go to History for other examples of his architectural creations. They are truly amazing.