A homonym has the same spelling and pronunciation as another word, but a different meaning. Cleave, meaning to cut, and cleave, meaning to join together.
A homograph has the same spelling, not the same pronunciation, and a different meaning. Bow of a ship, bow and arrow.
A homophone has the same pronunciation, different spelling, and a different meaning. To, too, and two.
I could not find a specific reference to a term where there are triplicate homonyms.
WikipediaAlan Cooper's Homonyms Let me know if you need more help with your question.
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