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VClip Collision Detection - "Planar edges"

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I have been reading the document ( www.merl.com/papers/docs/TR97-05.pdf ) and implement it.

I have almost succeeded, however I am having a few troubles with the EF/FF states;
I am not sure which one is the problematic, I keep getting into infinite loop where I keep changing from first feature to the second one,
and then back to the first one.

After debugging, I noticed something wrong with my topology;
That is, I noticed one of my edges contain a plane, which should contain the set of all points
that are closest to that edges, but isn't.

The problem is, I am constructing the polygon using Incremental algorithm (convex hull construction).
That is, the algorithm is creating triangles and not quadrants, even if they match.
e.g. for a cube, the result will be 12 triangles, and not 6 quadrants.

I was wondering then, how in such case I should handle.
As far as I can see, I have two options:

(a) quadrangulation (not sure how it's written); However, I haven't found any algorithm for it, and really not sure how to do so.
(b) Make the edge have the correct planes. The problem is, the edge shouldn't even have a plane.
The sets of points that are closest to the edge are all only the points above that edge.
Also, if that is the case, how can I represent and create such set of points?

Also, if anyone has any suggestion on how to correctly debug such an algorithm, I would be helpful.
The problem debugging such code is understanding the meaning of the values. I understand the code and what
it's supposes to do, but I can't be sure if it does it right or wrong because of the values, and something
the scene isn't clear enough.

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