From rounded domes to pointed cones, the forms by which vertical cylindrical walls are capped have been exhausted as far as the code is concerned. However, a re-examination of one option introduced a few posts back will expand upward possibilities greatly.
With the toroidal form, expanded elements intrinsic to the cubodal pattern were spun about one localized axis and essentially acted on equally intrinsic spheres displaced transversely from that axis.
Simlarly, parallel cubodal elements regarded in isolation as distinct entities and displaced from the central axis may be spun about any of their own axes to form the same cones, hyperboloids, ellipsoids, and paraboloids generated from the local axis.
Once fashioned, these forms are spun about the central axis and joined laterally by reason of the horizontal planes paralleling the earth’s surface at the intersection of intrinsic projecting cylinders.
All of this is to say that flat circular tops (and bottoms) are a legitimate alternative to rounded or pointed tops, and as such afford the bases by which cylindrical and other forms may be joined to build vertically extended structures in any way imaginable within the constraints of a particular cubodal orientation.
This brings us to another critical constraint. Derivations of cylindrical forms projecting from the earth were shown to be characterized by diameter-to-height ratios corresponding to the 4 cubodal orientations – with the edge, square, and triangle-up orientations diverging from the one-to-one proportion of the vertex-up. By reason of the natural line between vertex-aligned spheres and the point of contact between those spheres, the vertically-aligned cylindrical structure enveloping spheres so oriented may exhibit any diameter-to-height ratio.
As the vertex-up orientation is invariably present in guiding the foundation pad’s outer grid interfacing slope as an expression of inter or intra-grid junctures, the other 3 orientations may possess cylindrical forms of any ratio up to the one-to-one ratio. Beyond that, vertical walls must be a whole number multiples of cylinders proportioned according to the orientation employed, meaning there is a range of proportions between one-to-one and each orientation’s ratio that is disallowed. This rule applies to both initial and stacked external cylindrical walls.
Another way of extending a structure upward is supplied by vertical waves in which the maximum slopes are invariably 90° and appropriate cubodal angles are keyed to the minimum slopes. Like horizontal waveforms, their vertical complements may come in an integral number of quarter max-to-min slope sections. If the waveform’s terminates with both max and min points, either may situate at the bottom (or top).
Like horizontal waves, a different wave length may commence at another’s termination as long as it is keyed to the same (or inherent angled) slope. For vertical extension, triangle-up orientation supplies the steepest angles of about 55°and 71° to afford the maximum height-to-base area ratio. Like all other forms, vertical wave structure has its members pegged to the directions of the universal 24-point ring.
Thus are code designed towers guided to serve habitation, observation, mechanical (vertical axis wind turbines), hydraulic (water storage), and electromagnetic wave transmission purposes. As Part VII’s architectural phase is no complete, how the code’s conceptual model relates to electricity, magnetism, and light will be next.