As the envelope is made of paper, a mathematical model of its deformation would be an isometric coordinate transformation and thus must have zero 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)](http://www.spektrum.de/magazin/polyederkissen/822369).  
Maybe the same topic has also been treated a few month earlier in Scientific American.

The essential ressource is [Edouard Baumann](http://www.baumanneduard.ch), especially [this link](http://www.baumanneduard.ch/KI_jpg_inv.htm) (unfortunately in German only); there is also an image of such a polyhedral cushion.