http://www.math.columbia.edu/~woit/wordpress/?p=6260
Yesterday in QFT class the professor [0] explained the name by saying that the guy who came up with it was a "very good salesman". The reality is that probabilities can in a great deal of cases be expressed as the volume of something in some phase space, for a trivial example, consider the area under the curve between two x-values on the normal distribution's probability density function -- it's the 2-volume of a section of the Gaussiohedron.
So after branding quantum information science as the study of the "unitarihedron", Aaronson dragged out one of his more miraculous results, which is that PP is closed under union and intersection as a direct result of PP = PostBQP, where PostBQP is a complexity class derived from BQP using an idea called postselection. That proof was actually in his dissertation (if I recall correctly), written in 2006, and it was an extremely impressive proof which did not use a word like "unitarihedron" to describe its methods.
So, while it was a joke, if you read the article in the context of the physics community's reaction to the amplituhedron story, the included proof really just helps to drive the point home.
The methods now called "amplituhedron" have been under continuous development for the past ten years or so. My QFT professor[0] seemed sort of enthusiastic about the development. They do seem to represent a step forward in our understanding of quantum field theory, though the reaction of the media has been, in the eyes of some commentators, characteristically buzzword-driven.
