Is a penthouse allowed if the development plan requires a flat roof?

It must be said that new flat roof buildings are often constructed with internal pitched roofs, but the parapet (I think that's what the surround is called) is then executed straight.

But ultimately, that does not answer the question. A full story is defined differently in many federal states. For example, in Lower Saxony, the second story is considered a full story if 2/3 of the upper floor area has an average height of 2.30 meters; it is very well possible to build a setback story. It is all a matter of calculation.

Brief regards

Regarding 11ant b) I was not. I don't know any themed construction area. At all. I am learning that such a thing exists in Germany. I would never build it myself.

It must be said that new flat-roof buildings are often constructed with inwardly sloping roofs, but the parapet (I think that's what the surround is called) is then executed straight.

Parapet, yes. Flat roofs are rather shallowly pitched roofs anyway, otherwise drainage would be a bit of a problem.

What is supposed to be problematic about flat roofs is not clear to me. Our developer builds both gable and flat roofs and considers the latter less problematic.

I see it similarly. With the modern KfW cubes, it also seems more sensible to me to seal the "thermal envelope" watertight at the top right away, instead of faking a pseudo-pitched hipped roof on it, which creates a useless intermediate space and requires special tiles because it is so flat.

that new flat-roof buildings are often constructed with inwardly sloping roofs, but the parapet (I believe that is the name of the surrounding edge) is then executed straight.

Yes, that is the name of this trim (currently often as a built-up wall). However, these are usually flat roofs structurally, less often pitched roofs <10° pitch. Without roof overhang, the roof drainage is then "internal," which is even less trivial with pitched roofs.

If in Niedersachsen, for example, the second floor is a full floor, if 2/3 of the upper floor area must have an average height of 2.30, a recessed floor can very well be built.

This is probably about the two-and-a-halfth floor. So less about how to make the second a full floor, but whether another one may be above it. This here depends most critically on the eaves height, which counts practically like a story-high knee wall from its perspective.

This is probably about the two and a half storey. So less about how to make the second one a full storey, but whether there may still be one above it. The most critical factor here is the eaves height, which from their perspective basically counts as a storey-high knee wall.

Let's see. So here it says EH 111.175.

So here it says TH 111.175.

TH 111.175 would refer to NN; for that, one would need to know the corresponding height of the top edge of the finished floor on the ground floor. Or does it say TH1* 11.175 (that would be unusually precisely measured)? Then, starting from a zero point such as the top edge of the finished floor on the ground floor (or also a manhole cover or similar), 11.175 meters would be meant, which should easily cover almost three floors including base / terrain slope. *) This would only be usual in conjunction with TH2, i.e., either distinguished according to the uphill and downhill side of the property or if staggered shed roofs are also allowed.