Same Lists / Branches

I am trying to enumerate the number of unique panels which are all planar quads so they all same similar geometric characteristics.  I have extracted the least amount of information to describe the geometry, which is all the side lengths and one diagonal.

This gives me a branches with 5 items within each, as shown below.

Now all I would like to do is see which branches share the exact same data.  Quantifying the number of different branches and how many that have that same data. 

Each item must correspond directly: as in item 0 = item 0, item 1 = item 1, etc.

I know that I can see if they match 1 through a series of equality tests but don't know a work around to loop that test while culling out matched branches.

Any thoughts?