Tetrahedrons

It turns out I said something wrong in an earlier post.  I said that tetrahedrons would tile in space, i.e. fill up 3 dimensional space completely the same way cubes can.  Turns out that's wrong.  If wikipedia is correct, though, I'm in good company in my error, because they say that Aristotle believed it too. 
  It starts out with the idea that 5 tetrahedrons will make a pentagonal solid like the one pictured here.  Actually it's close enough that it works fine in beadwork, but as an actual matter of geometry the 5 tets would leave just a few degrees left in the circle.  Knowing that, I was aware, as I made this piece, that I had to tug just a bit extra to get the fifth tetrahedron to close.  Never noticed that before. 
  If the 5 tets did actually make the figure they seem to make, then 20 tets would fill an icosahedron, and you could keep adding on tets forever to fill space.  close, but no cigar.
  This probably has very little relevance in actual beadwork, since, as I said, it's close enough that you can pretty much make it work, but I had to mention it.