When it comes to the actual construction, then
amounts of materials, lengths of beams (for slanted
roofs and such) and so on come into play.

There would also be cost estimates based on materials.

Window sizes for example will affect temperatures and
change insulation requirements.

Closely related to the architecture will be the structural
engineering, especially for tall buildings. You want them
to stay standing, so wind force, required strengths of
materials, elevator capacities, and more need to be
figured.

For staircases, the steepness comes into play.
Spiral staircases are another story, too.

In climates where there is a lot of snow, the roofs
are steep so it doesn’t accumulate.

The more complex the building, the more math will be
required. For a standard house, not so much (but still
quite a bit). For a 100-story skycraper, LOTS !

Non-rectangular shapes bring in their own needs and
calculations, too.

.

Or maybe the Sydney Opera House? If I remember correctly, it’s mathematically interesting (though maybe not as much as the Arch).

Or if you want a little reading, I just searched google and found this (looks like it’s about several interesting buildings in Britain):