Commentary Par XXIV 22

Peter circles Beatrice three times, as he will do again at the end of the canto ([Par XXIV 152]), on that occasion circling Dante.  This number, that of the Trinity, is obviously auspicious.  (Some later commentators see it as the number of the three theological virtues; since Peter appears here as the representative of only one, Faith, that would seem a less likely reference here.)  However, and as other passages will remind us, it is also the number of times Peter betrays Jesus (see Matthew 26:34, 26:75; Mark 14:30, 14:72; Luke 22:34, 22:61).  This might not be a case convincingly made on the basis of this verse alone; but see C.Par.XXIV.124-126.