My house. A good looking mansard if I do say so myself. It's a little unusual for a mansard. The top window is rare. I've researched the house and believe that the third story/mansard was added on after the home's original build date of 1884. My husband's third floor studio features a chimney- not a stack, but a chimney.
We also have quatre sides on our mansard. Most of the local mansard roof lines are only seen on the front elevation and wrap just a little around to the sides; the roof is usually flat and slopes to the back to a single gutter. My mansard wraps around the entire house and the gutters are integated in the brick on all four sides creating
the most complicated, expensive and f-ed up gutter system encountered by local gutter experts.
Here is a rear view, including the AC unit which by code has to be non-visible from the street.