Let's say we have a shape with coordinates as $(X_1,Y_1,Z_1,X_2,Y_2,Z_2,\dots,X_n,Y_n,Z_n)$ in the 3D space where each point is connected to all other points.
Is there a way to estimate the volume that this shape occupies in space?
I believe this is a very general problem and there should be a famous theorem somewhere that pertains to it. Is it possible to solve for an exact solution analytically?