No. Shemini Atzeret is on the day before Simchat Torah.
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On Shmini Atzeret (aka: Shemini Atzeret) no work is permitted
for those practicing the Jewish faith.
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Sukkot starts on the 15th day of Tishrei. In 2009, this
corresponds to Oct 3rd. It continues for 7 days and is immediately
followed by Shemini Atzeret/Simchat Torah.
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All the Jewish festivities:Tu B'Shevat, National Holocaust
Memorial Day, Purim, Pesakh, Yom Hashoah, Shavuot, 17th of Tammuz,
Tisha B'Av, Rosh Hashanah, Yom Kippur, Sukkot, Shemini Atzeret,
Simkhah Torah, Hannukkah.
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Succos ALWAYS falls on the 15th of the Jewish month of
Tishri.
In 2010 ("this year" at the time of writing), Succos began on
9/22 in the evening, and ended on 9/29 at nightfall. It was
followed by the Shemini Atzeret holiday for the next two days.