To take advantage of the exceptional seeing above the boundary layer on Antarctic sites, a high-resolution telescope must be mounted on a support tower. An open transparent tower of framework minimizes the upward temperature-disturbed airflow. A typical minimum height is 30 m. The tower platform has to be extremely stable against wind-induced rotational motions, which have to be less than fractions of an arc second, unusually small from a mechanical engineering viewpoint. In a traditional structure, structural deflections result in angular deflections of the telescope platform, which introduce tip and tilt motions in the telescope. However, a structure that is designed to deflect with parallel motion relative to the horizontal plane will undergo solely translation deflections in the telescope platform and thus will not degrade the image. The use of a parallel motion structure has been effectively demonstrated in the design of the 15-m tower for the Dutch Open Telescope (DOT) on La Palma. Special framework geometries are developed, which make it possible to construct high towers in stories having platforms with extreme stability against wind-induced tilt. These geometric solutions lead to constructions, being no more massive than a normal steel framework carrying the same load. Consequently, these lightweight towers are well suited to difficult sites as on Antarctica. A geometry with 4 stories has been worked out.