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Why are there so many different ways to write the sound "η".  Why don't you use just one letter, like "η"?
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These were all pronounced differently from each other in ancient Greek. Greek speakers simplified the spoken language but the historical spellings remain. Newly created words tend to use ι in the middle and either ι or η at the end of the word, for example στατιστική (statistics).

There's another way to write the sound, the very rare υι.
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Chris is absolutely correct, I could not have answered better.

Thank you Chris!
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