As the envelope is made of paper, a mathematical model of its deformation would be an isometric coordinate transformation and thus must have non-zerozero Gauss curvature almost everywhere; that restriction is clearly violated by the cited solution of the teabag problem.
I already pointed out in a comment, that there was an article in the German issue (Spektrum der Wissenschaft, June 1995) of Scientific American, where the topic has been discussed here (in German).
Maybe the same topic has also been treated a few month earlier in Scientific American.
The essential ressource is Edouard Baumann, especially this link (unfortunately in German only); there is also an image of such a polyhedral cushion.