So, to make a long story shorter (and saner), I was helping Nathan with his AP Chem...and I was looking at the geometry for tetrahedrons. A very long and complicated page (here) discussed the derivation of angles and the like with the following paragraph (it does, incidentally, give a remarkable similar tone to the entire page--a flavor, if you will):
Note to teachers: if you build an octahedron and a rhombic dodecahedron off the octahedron faces (use the Zometool), and then attach a tetrahedron off one of the octahedron faces, the centroid of that tetrahedron will be the vertex of the rhombic dodecahedron. In fact, the distance from the centroid of the tetrahedron to each of it’s vertices is the edge length of the rhombic dodecahedron! Nature is not only beautiful, but also logical and consistent.
I got lost after "Note to teachers."
It was a long night.
Nathan wanted me to be sure to note that the author of this page and the subsequent paragraph derived the root angle of a tetrahedron (109.45) for those interested--FROM SCRATCH!
I officially feel dumber.