In the first case, the tetrahedron is skinny, and we distinguish five types depending on how its vertices cluster along the line.
Think of two congruent tetrahedrons made of differently pliable material.
We can even use (3.10) to define the local spaces for any diffeomorphic image of a tetrahedron.
We shall identify these curves, which might be thought of as forming a supporting framework for the tetrahedron.
The upper bound is based on a new charging scheme which assigns each tetrahedron of minimum volume to one of its four faces.
We normalize by scaling tetrahedra to unit diameter.
The sliver is the only type of small volume tetrahedron whose circumradius over shortest edge length ratio does not grow with decreasing volume.
In particular, the analysis is based on the singularities of these tetrahedra.
