Question: I made a story about a galactic tower of Babylon. The tower of Zarteqz is a huge tower in which different races are gathered and speak their own language. Confusion is common and once in a while creatures take off to space to give a fiery air to their litigations after which they return in better understanding.

Now I can just write that the tower simply exists and stands tall (like the gigantic buildings seen sometimes in sci-fi movies) but that's a bit too easy. If we assume the tower to be built on an Earth-like planet, how high a tower can be built? The materials at hand vary from diamond to megraphine, a material stronger than graphene not in all directions. It can be pulled, bend, and pressed with a very big force before it breaks or tears. It's too flexible though to really build a tower with. I was thinking to use a combination of the rigidity of the both. Diamond is hard but breaks "easily" while megraphine is rather soft and flexible but difficult to break.

How could I combine the two to make a tower as high as possible? Say that the tower has a base of a square kilometer and gets smaller to the top. Say the base has a circle form (as well as the rest of the tower.

I don't know how to rationally justify this but assume the wonder future material has three times the strength of graphene. It is in contrast to graphene a three dimensional material and can be cut with a laser beam.

For the properties of graphene look here (it has a huge variety of properties): <https://en.m.wikipedia.org/wiki/Graphene>

Answer: 
Unlimited height
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1. Your tower is a space elevator. It uses graphene to reach up to geosynchronous orbit .. and geosynchronous orbit can be very slow and hence very high.
2. Your tower is made of graphene elements that can be *charged* to varying degree. It has a tremendous amount of positive charge in the network of the middle layers, which repels the positive charges above and below it. Despite the natural instability of charges piled up in a line, with clever engineering, this is designed in such a way (relying on redistribution and conduction of charges based on strains in the materials) as to resist fluctuations and remain as a stable tower. Ideally any computer stabilization should be optional, since we can guess what will happen otherwise!
3. Your tower may contain superconducting rings (especially at high/cold altitudes) that magnetically repel one another or the planet's magnetic field.
Nearly unlimited height, different approach:

I do not believe you can support such a tower with electric charge. However, there are two other approaches to use here:

1. Space elevator. You don't give a strength for your megraphine so whether this can be done or not can't be answered. Assuming the material is strong enough to support an elevator on Earth (your restrictions on it are fine, it's going to be used purely in tension) you **must** go out to beyond 35,786km (geosynchronous orbit) and beyond that either requires a counterweight or to be extended to IIRC around 170,000km.

If you can clean up space this is viable with materials with strengths similar to carbon nanotubes. You can't go much below that without the cable getting very fat in the middle, though--the taper of the cable is extremely sensitive to the strength/weight ratio.

2. If you don't have the materials for this there's also the space fountain. It **must** be less than 35,786km. You throw magnetic material upwards at extreme velocity. The top of the tower sends it past a magnet to direct it back down--and the base likewise sends it back up. Every floor or group of floors extracts energy from the bits heading up and uses that energy to push on the bits heading down.

All the magnets involved must be superconducting and the bits must be traveling in a very hard vacuum--they are going to be moving **extremely** fast. There are no material strength requirements for this, but your engineering had better be **extremely** reliable.