What's the connection of the symbol of "unicorn," uniqueness, in The Glass Menagerie to its symbol in ancient and medieval origins?

I think that the distinctive qualities and the uniqueness
of the unicorn is set against the idea that it is different from the other horses.  In
my mind, this becomes one of the fundamental elements to the discussion in the play. 
Those who are different because of unique talents, special qualities, and distinctive
features are nonetheless different.  Williams seems to be making the argument that there
is a certain pain and burden to be carried in being different.  It might be comforting
to consider that one is better or superior because of their differences, but the reality
is that there is still difference from others, and this can be difficult because of the
lack of assimilation present.  Laura is like this.  She is different from others and
this is what makes her so special.  However, there is a certain frustration evident
because of this difference.  She experiences frustration because she is not like
others,and seen as a "freak."  Regardless, that like the unicorn, she possesses
qualities of this world that represent what can be as opposed to what is.  Like the
unicorn, she possesses a sense of magic in how she is able to endure the challenges of
her world and even transcend them.  Yet, in the end, when the unicorn breaks, she is
able to argue that it no longer looks "freakish."  In this light, being different is
something that is a challenge, something that can be alleviated when one no longer is
different.  Considering how Williams perceived this idea in his own life, it becomes
powerfully poignant.  He understood that one of the biggest mistakes of his life was not
stopping the lobotomy that his sister received, a procedure designed to make the patient
less "freakish."  In the end, Williams might be reminding us that there might be a
certain convenience in being like others, and not being as "freakish," but the long term
results are disastrous.