the corners of the central roof opening. The upper ends of the valley rafters rest on the wall, and the bottom ends on the horizontal beams. The smaller rafters rest their upper ends on the wall, and their lower ends mostly on the beams and cross-beams; the short rafters in the mitered corners of the roof rest on the valley rafters. Tetrastyle cavaedium In the atrium tetrastylum additional support was required in consequence of the dimensions of the hall; this was given by columns placed at the four angles of the impluvium. This style is not common in Pompeii. These pillars support a beam, which supports a wall, which in turn supports the rafters in the middle of the atrium. There is no need for horizontal beams spanning the entire room; the rafters have shorter spans. This allows a larger room to be roofed. Corinthian cavaedium This style has a rectangle of pillars around the roof opening. It is like the tetrastyle, but with more than four pillars. It resembles a peristyle. If the lower layer was sufficiently robust, it could support a second story. Displuvial cavaedium In this style, the roofs, instead of sloping down towards the compluvium, sloped outwards from the compluvium, the gutters being on the outer walls; there was still an opening in the roof, and an impluvium to catch the rain falling through (and presumably fed by the gutters). This species of roof, Vitruvius states, is constantly in want of repair, as the water does not easily run away, owing to the stoppage in the rainwater pipes. This type was rare; only one had been found in Pompeii, . Testudinate cavaedium The atrium testudinatum was employed when the atrium was small and another floor was built over it. The name comes from the Latin word , which means a turtle or tortoise, and by transference a covered vault. The Encyclopædia Britannica said that no example of this type had been found at Pompeii, . While narrow homes had atria that were not flanked by cubiculums and alae, and even atria where the impluvium was set against a wall or in a corner, homes smaller than 5 meters across are generally testudinate. Proportions Vitruvius continues by giving the correct proportions for an atrium (length:width ratios for the atrium, and their proportion to that of the opening in the roof, width:height ratios for the atrium, and the