As noted building high tower is not feasible in practice. Pyramid though would be much more feasible. It is only 1/3 weight of equivalent tower (polyhedron that is cube) so can be theoretically 3 times higher while simultaneously way more stable. Though if high, curvature of earth has to be considered as well since the lengh of base edge is equal to height.
I like the pyramid idea for one other reason, none of the tower ideas are feasible outside of a vacuum. How much stress is applied to the brick from even a slight wind? Torque to the structure at varying heights because of the wind?
Since LEGO™ pieces are pretty uniform and there are known pieces, it seems that the engineering math would be easy enough. Once someone has done the work of transcribing the 1x1, 2x1, 2x2, etc pieces and plates into a LEGO™ Calculator.
I am sure these already exist in a minimal form to help pack a cup with LEGO pieces when you buy them from a LEGO™ store.
