With the direct hit made by the rectilinear column projected from the center of the celestial co-cube to a hypothetically specified location on earth’s surface, familiar vertical and horizontal lines characterizing the projection were emphasized from the ground view.
The manner in which the co-cube column’s leading horizontal plane merged flat with the surface was in direct contrast to the earth-facing plane of the prime cube’s column (shown below left) which alighted at variable incident angles according to latitude. The co-cube’s column - projected from the center of the earth facing square (as shown below right) – landed such that its very center touched down to the surface first - flat and tangentially.
The center of the co-cube’s projected column represents the intersection of lines inherent to the square’s pattern. Because the lines are oriented with the cube and its cubodal square foundation’s orthogonal alignment with respect to earth, those lines correspond with the conventional lines of latitude and longitude.
This convention, though artificial, is actually quite attuned to nature in a very fundamental sense. Lines of latitude and longitude, like those hypothetically imposed on any spinning sphere (which just about characterizes every individual object observed in the sky, night and day) correspond to the tangential direction of earth’s poles (north and south) and its rotation (east to west). Thus is the rectilinear grid superimposed by the co-cube column’s leading earth-facing square termed the polar-rotational grid, or P-R grid for short. Grids so-oriented are not uncommon in the US or Canada, although pretty rare everywhere else.
Although orthogonal lines intersecting the center of the column’s leading square are named to delineate the grid, in practice those near to the centerlines may be considered parallel and employable. However, as measurements made on the ground to delineate a hypothetical structure grow in scale, they increasingly diverge from earth’s natural P-R lines - the further from the equator the more so as longitudes converge and the currvatures of latitudes tighten. If vertical planes following the earth-facing square’s more distant lines were to slice through the earth, viewing the segments formed directly would reveal sharper divergence from a rectlinear grid than those closer to great circular arcs made by lines closer to the square’s centerlines. For this reason are the projected columns specified to be narrow – with their cross-sectional areas small.
Technically, the lines forming the leading square’s central intersection will invariably be off a bit at any given time due to the roughly circular periodic wobble of the earth’s axis; and the general drift of its average position. These are interesting phenomena, but like the divergence between projection lines and circular arcs noted above, their practical effects are too miniscule to be factored into a tape measurement, even if planning the layout of a structure intended to last a 1000 years along the coasts of the Arctic Ocean or continent of Antarctica. Observing these matters serves: as a reminder of the calculus-evoking reality posed by the rectlinear meeting curvilinear space; to allay concerns regarding any practical consequences; and to simply underscore why a well-aligned smaller abode stays truer to both the projection and earth’s natural lines (arcs) than a larger one.
The polar-rotational grid defines the pattern and orientation of the code’s cube-based architecural scheme. Though it can be expanded to the realm of planning with the infrastructure of roads, utilities, etc., as has already been the case in many locales, it is not required for the cube-based home to lie within such – as far as the code is concerned. Other building codes and zoning laws might prevent or require such adherence, but as far as this code goes, it can either stop at the abode and merge with nature or non-code designed landscape, or organically expand via ground shaping and beyond.