Dr. Bisson recommended looking at the following:
It mentions an interesting problem (DGP). Given six points, A, B, C, D, E, F, we can ask some questions:
  • are there six edge lengths for a possible degenerate tetrahedron?
  • does the tetrahedron have zero volume and thus lie in a plane?
  • if so, which corner lies inside the triangle of the other three corners?
There are degenerate versions of the last of these questions, since three corners may lie in a line.
We think that there are good answers for these questions, and they should help us understand collisions in stick robots and stick knots.