No, they all have their own eyes.
You are thinking of the Graeae, three archaic goddesses, daughters of Phorcys and Ceto. They looked like old, grey-haired women and had only one eye and one tooth
to go between them.
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The Fates are 3 old women but they can change shape if they want to. No one can change the Fates as they are what they are.
There were three fates.
The Fates control destiny, and who lives and dies.
The Three Fates were the goddesses of time of life. One of them spun your thread of life, an other one measured it, and when you die, the last one cuts your "life line". So in short, they control when you are born, how long you live, and when you die.
No, you're thinking of the graeae