High-resolution telescopes require a mechanical stability of fractions of an arc second. Placing such a telescope on top of a tower will improve the local seeing. An open transparent tower of framework minimizes the upward, temperature disturbed air flow. The tower platform has to be extremely stable against rotational motions, which have to be less than fractions of an arc second, unusual in mechanical engineering. Active systems can improve the stability. However, they need sensors for position measurements, active actuators and a control loop. The performance is limited by the available signal-to-noise ratio. Consequently, improvement of the passive stability of large tower structures will significantly contribute to the final stability. Special geometries in steel framework can reach extreme passive stability of a tower platform, particularly against rotational motions. There are several groups of basic geometries, which lead to solutions and we will give a systematic description. The proposed towers can be welded or screwed together from smaller parts. This makes a construction in adverse environments like the Antarctic region within good reach.