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The 3-5-2 has been popularized in Italy by teams like Napoli and Juventus, who have used it to great success over the last few years.
The thing that makes this formation so attractive currently is that the bedrock of the formation—the back three and goalkeeper—all come from the same team.
Gianluigi Buffon, Andrea Barzagli, Leonardo Bonucci and Giorgio Chiellini have been playing in the 3-5-2 for Antonio Conte at Juventus for the last season-and-a-half and by this point must know each other like the backs of their hands. De Rossi played in the center of the three-man line in the first two games of Euro 2012 when Barzagli was hurt, but it's far better for the Juve foursome to play together.
As an added bonus, the three-man defensive line allows Prandelli to put Barzagli, Bonucci and Chiellini—all of whom are amongst the top 15 to 20 center-backs in the world—on the field at the same time, rather than decide which of the three to sacrifice when playing with two center-backs.
Don't think that he could bypass this choice by using Chiellini as a left-back, because he's far beyond that at this stage in his career. Granted, Brazil 2014 will probably be the last major international that Barzagli will be young enough to participate in. Still, this formation is the only way that Prandelli can get these talented defenders on the field at the same time.
The central midfielders have pretty much the same responsibilities as the rear three do in the 4-3-1-2. The one in the center doesn't necessarily have to be a pure regista, but it certainly helps. In Prandelli's version Pirlo and his heir apparent Marco Verratti generally operate the same way they would in the 4-4-2.
The lack of a central midfielder in a more forward position does necessitate one of the strikers being more of a creative type, like Cassano, as the forwards will have to do more of the creating on their own with the line of supply being a bit farther away.
The main weakness of this formation is the lack of adequate personnel for the wing-backs. Napoli's Christian Maggio is probably the most natural fit in the Italian player pool, but at 30 years old, he is pushing the age that internationals are normally put to pasture.
The situation is even murkier on the left. Emanuele Giaccherini was used on the left in the two matches that used the formation in Euro 2012, but he's spent his entire career as either a winger or a mezz'ala, and his inexperience was apparent. His misplay in the group stage opener against Spain allowed Cesc Fabregas to get inside him to score the equalizing goal.
Domenico Criscito is among the best in the world at his position, but he's more of a traditional left-back, as is Federico Balzaretti, who is also at an age where he won't have much more time in the national side.
A final note against this formation is that it involves a heck of a lot more running than a more traditional four-man back line. With all the extra effort that is expended by players who aren't necessarily used to it at the club level, it may end up leaving Italy vulnerable late in games.