In the Western Ashkenazic rite, a different piyyut is recited in place of this last one, see Daniel Goldschmidt and Yona Fraenkel, Sukkot Machzor, pages 427-430. In the Sephardic rite, a completely different set of piyyutim is recited. In most contemporary Sephardic communities, as well as many Ashkenazic communities in Israel, these piyyutim are recited before Musaf instead of in the middle of Musaf.
