  Here we explore a variety of properties of intrinsic flat convergence. We
introduce the sliced filling volume and interval sliced filling volume and
explore the relationship between these notions, the tetrahedral property and
the disappearance of points under intrinsic flat convergence. We prove two new
Gromov-Hausdorff and intrinsic flat compactness theorems including the
Tetrahedral Compactness Theorem. Much of the work in this paper builds upon
Ambrosio-Kirchheim's Slicing Theorem combined with an adapted version Gromov's
Filling Volume.
