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as i have mentioned before, i will focus on the outer shell of the kunsthaus, but the text will not feature an in-depth coverage of the museum and the multitude of viewpoints you can have on such a complex building.

some thoughts about the geometry of the shell
'shell', 'free form', or 'organic form' are terms that are being used to describe a certain species of shapes that seems to follow roughly the same concept. but in fact the way different shapes are organized and what is their underlying philosophy can be very far apart. it may not be complete as a categorization, but let us look at three different types: 1) 'organic' structures in the true sense of the word always resemble the forces that are placed upon them and they rather emerge instead of being manipulated by design. this is the principle that applies to everything that is part of living nature. the process begins when liquids form thin films due to surface tension and then harden to a certain degree.

this is how cell structures, the shells of crustaceans, or bones are being formed. they strictly follow the rule that the elements within the structure are organized in a way that, as a result, stresses are equal at any point of the structure. this rigid framework does not allow a designer to impose arbitrary changes on the structure; in that sense the emerging structure may not be called a 'free form' at all.
in architecture, membrane stuctures and pressurized structures are the most typical example for this approach - see the books that have been published by the institute for lightweight structures in stuttgart.

2) opposed to this buckminster fuller's concept of the geodesic dome is situated in an ideal environment with no defined direction of gravity (mostly because it is itself the center of gravity) but takes origins from a bundle of philosophical threads that include cartography and navigation, atomism and economy. see my page about fuller here.
3) and then there is the new freedom that came from the computer's ability to handle mathematical curves very well.

this option was not available for designers from the very beginning. you may remember the pixelated appearance of typefaces before postscript came (by the end of the 80s). way before, amongst the first companies to adopt computer-aided-design were automotive companies. elements in heavy machinery are mostly straight lines or circles, but cars there are all types of curves. so pierre bezier worked on that problem in the 1960s for renault (he was head of the tooling department) and pioneered cad/cam techniques for curved surfaces. up to now a wealth of software that can manipulate curved surfaces has become commonplace.
in architecture this new freedom now triggers a multitude of postrationalizations that seem to owe their existence to the adoption of paradigms quite arbitrarily taken from other intellectual disciplines - from soliton waves to chaos theory.