[Image taken from Allison, Penelope M. "Domestic Spaces and Activities." In The World of Pompeii, edited by John J. Dobbins and Peder W. Foss. New York: Routledge, 2007.]
At the sides of the atrium could be found several small rooms known to modern scholars as cubiculae.** At the end of the atrium farthest from the door there were usually two spaces, not quite rooms as they weren’t walled off, in line with the cubiculae. These were known as alae, or “wings.” A triclinium (dining room) sometimes opened onto the atrium as well.
Beyond the atrium was the tablinum, which could be described as the office. This was where the master of the house did business. It generally had a view of both the atrium and a peristyle garden deeper within the house. The garden itself was usually surrounded by a colonnaded walk, on to which opened smaller cubiculae. A triclinium might also be found back here.
This is only a basic framework, open to a lot of variation. If the family was wealthy enough the house might have a separate service area (kitchen etc.) where slaves worked, sometimes with its own atrium. It is also possible that some upstairs rooms had a similar purpose. Some houses had two atria for the use of the whole household or only had cubiculae on one side of the atrium. A house matching that exact floor plan up there probably didn’t exist.
*Our major sources on what Roman houses actually looked like. We are not as dependent on these cities as we are on Olynthos for knowledge of Greek houses, but they do make up a sizeable chunk of evidence.
**This is one of those “we don’t really know for sure, so we’re going to call it by a general term that we know fits” kind of deals. It’s literally “a small room.” Some would call them bedrooms, which would not be entirely inaccurate if only because people did sleep in them, but they were used for many other things as well. Only the very wealthiest could afford to have a room primarily for sleeping in.
Vitruvius, De Architectura (Book VI) - Project Gutenberg
Allison, Penelope M. "Domestic Spaces and Activities." In The World of Pompeii, edited by John J. Dobbins and Peder W. Foss. New York: Routledge, 2007.
Wallace-Hadrill, Andrew. Houses and Society in Pompeii and Herculaneum. Princeton, NJ: Princeton University Press, 1994.