Kirby Urner says: >The choice of shape was cultural / conventional, not dictated by any deities nor by logic, and in fact we may develop a consistent mathematics by following this other branch, and in fact we have. >Which is another point to make: that mathematics is a process of branching and sometimes merging (like in Git).
I don't see it quite like that -- it seems more like a choice of "unit". And if nothing else (though I'm sure there is something else) it demonstrates nicely that the relationship between volume and linear measure doesn't depend on cubes.
One thing that recommends the rectilinear approach, and is quite useful at times, is that it lends itself to an easy to understand coordinate system. Or is there a nice one for the tetrahedrons that I'm just not seeing?