If the second floor is not built in the ground floor, the building depth equals the width.

You rarely read "Verkappt" in official documents either...

So the regulation is not that complicated. They want, as is common in the area, 1.5-story houses. But since it is also modern up there to build these so-called city villas, they want to anticipate individual exemptions and say 'Yes, you are allowed to build a city villa'. These are usually square. So they could also have written 'Allowed to be built are 1.5-story single-family houses, except for square city villas with a side length of up to 12m, which may be built with 2 full stories'. I guess there will also be a rule somewhere regarding roof shape/pitch as well as knee wall height. Otherwise, according to the known excerpt, one could also simply build a 2-story building with a flat roof, then the 2nd full story would be the attic, and the regulation to build it square would be circumvented.

Yes, but why?
So is a square city villa less conspicuous than a rectangular one?
Does a very influential person in the development plan committee have a phobia of tenement blocks?
I actually think rectangular would add a loosening effect to the mainstream "modern" design of city villas, which would even fit better in a rather classical single-family house settlement.
But I am no longer surprised by local politics in D, otherwise I would have chronic whiplash from shaking my head.

Yes, but why?

It's right there. If the substitute villa is wider than it is deep, it looks like an apartment building. o_O:rolleyes:;)

Otherwise, according to the well-known excerpt, one could simply build a two-story building with a flat roof; then the second full floor would be the attic, and the regulation requiring it to be built square would be bypassed.

Exactly, but that would only work to a limited extent with a flat roof; better with a shed roof or gable roof, with rooms open at the ridge, so that there would be no disputing the attic status of the upper floor. I would probably do it that way just for fun: a legally fully compliant nonsensical regulation with maximum trickery enjoyment :-)