On Wed, Jul 17, 2013 at 9:24 AM, Joe Niederberger <niederberger@comcast.net> wrote:
R Hansen says:
>Thus, it isn't a mapping of volume like the cube.

<< SNIP >>
But it seems the underlying math will be generally be what we are all used to, all that conventional stuff.
Or, prove me wrong, I'm no expert here, just a guess.
But that's why I said I don't see this as a whole "branch" of mathematics, the way Kirby put it.

Here's an unconventional non-XYZ mapping:


This new book Divided Spheres gives more of an up to date bibliography:


The tetrahedron-as-unit-volume guy was also the geodesic dome guy, so lots of connections, lots of developers:

... Arthur Loeb, Amy Edmondson, Joe Clinton, Ed Popko, J. Baldwin, C.J. Fearnley, me, E.J. Applewhite, Russ Chu ...

(some living, some not)

With tensegrity added, you get Kenneth Snelson, whom I've enjoyed some time with, great guy.  His work inspired Elastic Interval Geometry, a great way to learn about vector addition and animation:  ... Tim Tyler, Gerald de Jong ...  http://springie.com/
Assigning unit volume = 1 unit sided tetrahedron may make some calculations easier, so why not?

Joe N

Remember the flagship organic chemistry journal is named Tetrahedron.