I've recently come across some mid-sized 3-manifolds that I think are likely hyperbolic, but SnapPea has some trouble with them.  This is related to my previous question

http://mathoverflow.net/questions/4918/can-you-fool-snappea

but in this case I'm dealing with closed, orientable 3-manifolds instead of knot and link complements. 

The 3-manifolds I've come across have 11, 12 and 13 tetrahedra in their triangulations.  One of them SnapPea finds a solution to the gluing equations but it has "negatively oriented tetrahedra".  Does this mean what I think it means -- that once you've put the geometric structure on the tetrahedra, you have a tetrahedron folded-over?  If you view the gluing equations from the upper half-space model, they say that the sum of a bunch of angles should be $2\pi$.  Is this the case where one of those angles is negative? 

The other two triangulations SnapPea finds geometric structures with degenerate tetrahedra.  In the upper half-space model this is where one of the angles is zero, I believe. Is there a way to fix this, so that I could get a Dirichlet domain, drill and fill, etc?   This is my primary question. 

Here are the triangulations, both in SnapPea format and Regina format. 

[Regina file, all triangulations][1]

[11-tet, SnapPea][2]

[12-tet, SnapPea][3]

[13-tet, SnapPea][4]

With the 12-tetrahedron example, SnapPea can generate a Dirichlet Domain.  This one has what looks almost like bevelled-edges.  Is there a way to find a better basepoint to grow the Dirichlet domain from? 

![12-tet Dirichlet domain][5]


  [1]: http://dl.dropbox.com/u/46424505/triangulations/found_hyp_tri.rga
  [2]: http://dl.dropbox.com/u/46424505/triangulations/tri11
  [3]: http://dl.dropbox.com/u/46424505/triangulations/tri12
  [4]: http://dl.dropbox.com/u/46424505/triangulations/tri13
  [5]: http://dl.dropbox.com/u/46424505/triangulations/pic.png