In a traditional machzor, during yom kippur, how many time does the congregation say the "al cheit" set of players?
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On Yom Kippur itself it is said 8 times: [in parentheses I have placed the page numbers from the Artscroll Machzor Zichron Yosef]
In ne'ilah we only say the Ashamnu list twice, not the al cheit section.
Note it is also recited by the congregation on Erev Yom Kippur in the silent amida of mincha.
If I missed any, I hope someone adds to this. Note, I included all the times when al cheit could be said by a member of the congregation. I wasn't sure if the question wanted to know all the times al cheit is said by the congregation as a congregation, or all the times when someone in the congregation would say the litany.