The Turner Syndrome symbol is the butterfly.

Here is the history of the symbol, according to the Turner Syndrome Society (TSSUS):
"The four circles from our previous logo have evolved into the wings of the butterfly. This evolution connects our past to our present. The butterfly is feminine yet strong like our members. Every butterfly is unique just like our members. Butterflies fly on their own which is what we hope all of our members will do with the help of TSSUS!"

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