quickfur Wrote:But regarding polyhedral volumes... isn't it just a matter of dissecting the polyhedron into right pyramids and summing them up? This isn't too hard to do from the vertex coordinates.

But that dissection can not be really expressed in a formula (rather in an algorithm). To illustrate, consider the following.

Out of curiosity, I once computed the area of a triangle given by the length of its sides (you know it is determined by that data) and got the following (seemingly unknown) formula:

(Ok, I see thats not exactly what I asked before, but nevertheless the topic is general enough)

It seems for me that every simplex is exactly described by the set of its edge lengths. So how is the general formula for the n-simplex?