While the atrium and tablinium appear, both in the roots of their names and their functions, to be Roman in design, the peristylium appears to be directly influenced by Greek architecture, and its name is Greek in origin. As the atrium was the focus of the front part of the Roman house, rooms in the back part were grouped around the peristylium.
Marcus Vitruvius Pollio, in his book, De Architectura, gives the dimensions of the peristylium: "The cloister (peristylium) is transversely one third part longer than across. The columns are to be as high as the width of the portico; and the intercolumniations of the peristylia are not to be less than three nor more than four diameters of the columns. But if the columns of a peristylium are of the Doric order, modules are taken, and the triglyphs arranged thereby, as described in the fourth book."
Simililar to the atrium, the peristylium was open to the elements, but rainfall watered the garden plantings instead of falling into a pool or impluvium. The gardens might be decorated with statues, frescoes and an elaborate fountain, or piscina.
Several rooms opened into the colonnades surrounding the peristylium, including triclinia, cubiculae, pantries, store-rooms, and an oecus, which served as a second tablinium or state-room.
References: Handbook to Life in Ancient Rome, Lesley Adkins and Roy A. Adkins (Oxford University Press, 1998); The Romans, their Life and Customs , E. Guhl and W. Korner, Senate Press, 1994