The first tower (left-hand picture) is vaguely inspired by a building in Madrid whose official name is «Torrespaña», although it has been nicknamed by the people as «El pirulí» (a cone-shaped lollipop).
Both platforms rest over the regular hexagon formed by the top six shaft balls. In the first tower, the platform widens to a regular 24-agon, over which 24 vertical «windows» are built, and then narrows to the base of the mast.
In the platform of the right-hand tower, the 24 square perimeter «windows» of tower number 1 have been replaced with a bigger and more elaborate structure.
It is impossible to build a truly conical shaft, so we approximate its shape making it in three stages, each one eight levels tall. From a double-scale regular hexagon, to an intermediate non-regular one (edges of alternating lenghts 1 and 2), to a single-scale regular hexagon.
In the following pictures, we illustrate the shaft building process, such as it was done for these towers, and on which our piece counts are based. Obviously, there are many other possible building methods. We were trying here a design that was relatively cheap on rods and square panels, without losing much strength.
Two more detailed views of the platform in tower 2:
In principle, any stable structure which can rest on a regular hexagon could be used as a platform. We illustrate here two trials. On the left, we tried to extend the platform of tower 1 horizontally, mixing three instances of its structure. Although I liked the outcome, it is very fragile, and I was never able to close it with a fitting «roof». The structure on the right was intended to be a spherical, not too heavy platform. But it also collapsed at every completion attempt.