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From 49 to 58, depending on the style of princess cut identified.

From Wikipedia:

"The name 'princess cut' was originally used in connection with another diamond cut, otherwise known as the 'profile' cut, designed by Arpad Nagy, a London cutter, in 1961. The same name was later used and made popular by Ygal Perlman, Betzalel Ambar, and Israel Itzkowitz in Israel in 1979. A similar cut with only 49 facets, as opposed to the original 58 facets of the princess cut, was later branded the 'Quadrillion' and initially distributed by Ambar Diamonds in Los Angeles."

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