## Dueling Grids

As universally useful as the linking schemes of Polytechnic Integration are, they also have a dry and abstract flavor, all the more so for lacking the tangible relevance they might hold engineers. From my perspective as a non-engineer, what has motivated me to develop the schemes is their logical beauty and how this gave rise to an applicability explosion from just a few principles embodied in a few simple shapes.

For all that, I have (IMHO) saved the best for last: The integration of cube and bode, or in down to earth practical application terms, abode and earth. Therein lies the code’s contribution to the landscaping arts, and in the context of the code, the integration is big enough to get its own part (V) entitled Ground Design. Unlike polytechnic integration, its subject matter can be pictured by most, and it is in the realm of applicability for many – the shrinking middle class and the kind of home ownership that comes with a little piece of land notwithstanding.

Ground Design begins with a bird’s eye view of the rectilinear grid lines etched 2- dimensionally onto earth’s surface. In Cube-based Abodes, the polarrotational grid was introduced as the setting for the code’s signature building scheme – aptly dubbed humble cosmic architecture. The P-R grid’s alignment is very familiar, and very naturally corresponds to longitudinal (north/south) and latitudinal (east/west) lines following the projection of the celestial cocube perched atop the geocentric cuboda’s equatorial square.

The geocentric cubodal shell also bears – within its geometry – another grid orientation. To see how this is so, the shell undergoes primary longitudinal rotation such that its equatorial square situates at a longitude ninety degrees from that of a specified location.

So positioned, the cuboda poses a pair of skewed squares over the location’s longitude, with those squares each having opposing corners that coincide with a pole and and an equatorial vertex. These squares are rotated latitudinally about an axis that passes through the center of the pair of opposing squares straddling the equator.

With such secondary rotation, the center of the skewed square may be positioned directly over  location. As such, the square’s lattice poses a potentiality of superimposition on earh’s surface that constitutes an alternative diamond grid whose lines run northeast to southwest and northwest to southeast.

Although the P-R grid is commonly represented in large Anglo American cities and the great Midwest farming region, the diamond grid is rarely seen beyond Washington DC’s  boundaries, and baseball diamonds in their own worlds.

How diamond and P-R grids integrate is guided by the model comprised of the geocentric cuboda and the appended celestial cube. If one were to follow the cuboda’s radial lines outward from the center to meet the cube’s corner, a 135° turn is required to continue an upward and outward trajectory along the cube’s unshared edge.

Thus 135° is the angle made transitioning between grids. The code disallows sharp 45° angle junctures between grids. Within each grid, 90° is of course the only turning angle.

Aside from the smooth sensibility of such a rule, the basis of the rule can give one an abstract sense of how a true, sublime, and practically impossible integration between cube and cuboda can be visualized – and how the meaning of its metaphor might be characterized.