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Councils in which the pope is represented by legates are, indeed, also representative of the whole teaching body of the Church, but the representation is not absolute or adequate, is no real concentration of its whole authority.
Councils over which the pope presides through his legates are not identified with himself in the same degree as the former.
The infallibility of the council is intrinsic, i.e.
Council of Vienne, (1311–1312) - Disbanded Knights Templar
Council of Siena, (1423–1424) is the high point of conciliarism, emphasizing the leadership of the bishops gathered in council.
Council of Trent, (1545–1563, discontinuously); response to the challenges of Calvinism and Lutheranism; imposition of uniformity in liturgy in the Roman Rite (the "Tridentine Mass").