What do I call a building with a variable number of storeys?

Solution 1:

I suggest the term asymmetrical, though it would require follow-up explanation. "The city block is comprised of one asymmetrical building that is divided into sections of varying levels."

Solution 2:

There's no such thing; here's why:

If it's a single building, as you say, then the total number of stories† doesn't change. The total is the total. A building may be, for example, seven stories on one side and only five on another, but we would nonetheless say it's a seven-story building because the total number of stories remains seven. Part of the structure being fewer stories doesn't decrease the total number of stories the building has.

Willis Tower in Chicago is 110 stories. The fact that it has sections that are only 50 stories, 66 stories, and 90 stories doesn't diminish its count of 110 stories or lead anyone to call it anything other than a 110-story building. That would remain true even if there were a hole creating a giant courtyard, as it were, in the middle of this building that takes up an entire city block.

That said, if you wish to clarify that there are sections that have fewer stories, then you simply say that. You could say something like, "The block is a courtyard building whose north tower has seven stories and whose remaining towers have five."

† I'm American, so I'm using the American spelling "story" rather than the British spelling "storey," along with the American plural spelling "stories" rather than the British plural spelling "storeys."

Solution 3:

What do I call a building with a variable number of storeys?

The general design concept of the Solnechny city district provides for the construction of City Block 1.3, a perimeter block with a variable number of storeys.

If I am understanding this correctly the translation means, a perimeter block where the (variable) number/amount, of storeys can be changed I presume this item of change is regarding one building can be of a different amount of storeys than an adjacent building. Rather than in the afternoon it has more stories than in the morning.

In which case I think a better translation would be

a perimeter block with a undefined number of storeys.

undefined; Cambridge English Dictionary adjective: not clearly described, stated, or known:

The general design concept of the Solnechny city district provides for the construction of City Block 1.3, a perimeter block with a undefined number of storeys