The idea of a universal intermediary embodied by the sphere ultimately materializes in the integration of earth (within its bodal context) and the cube-based abode architectural style which is viewed as the nucleus of a cell that nourishes it.
View the Gallery to get a sense of ground design possibilities, and the PDF for step-by-step derivations, the simplest of examples, and complete application guidelines. This page of introduction is organized into 4 sections, with underlined terms signifying glossary entries.
Dueling Grids – 1
To specify how grid constructs are shaped, an alternate grid is defined to join the polar-rotational grid etched by the celestial cube projection to align with the cube-based abode, and conforming to lines of longitude and latitude. The alternate grid is also abstracted from geocentric cuboda squares – specifically those skewed ones pegged to the poles, the equator, and equator-straddling square corners.
The orthogonal lines of the skewed squares’ innate patterns superimposed onto earth’s surface constitute what is termed a diamond grid. Its lines extend from northwest to southeast and northeast to southwest. To integrate the 2 grids, a cue is taken from the cubed geocentric cuboda, that is the angle between a line radiating from the bode center (of earth) and the outward bound celestial cube edge joining it.
The Bodal Prism – 2
To shape earthen constructs 3-dimensionally within the contexts of the 2D grid types, the bode is conceptualized as a prism in which the white light is analogous to natural terrain split into a quantized set of specific waveforms – the most elegant transitioning curvature between one level and another. As the bodal prism is a local representative of the geocentric cuboda, it is likewise aligned in accordance with whatever bode oriention is good and proper. However oriented each prism is characterized by symmetrically sloping planes and lines.
The angles of the prism element slopes are then keyed to the unique points of maximum slope that characterize any wave’s shape. The criteria in selecting which prism and which of its sloping element to use include practicality; distinguishing the construct in its grid context while allowing for harmonious connect-ability; elegance; and finding a symbolic match between the bode element and construct’s grid role. E.G., as bode vertices signify junctures between bode squares, so junctures between grids are shaped by waveforms keyed to the vertex-up prism’s sloping edge.
Cellular Landscaping – 3
In the analogy of a cell alluded to in the introduction above, CBA architecture ascribed to the nucleus is immediately embarked with waveforms keyed by the square-up prism because it most conforms to the P-R grid that the walls arise from, and rotated, its octahedral geometry nests the corners. By keying prism lines’ 45º slopes to embanking half waves, a universal average to every complementary roof slope combination is posed at every latitude. Beyond this default, optional slopes are reasonably found in other prism elements for use on inside and outside corners.
Proceeding outward and apart from the abode, the waveforms of P-R and diamond grid berms are specified from edge-up prisms aligned to follow either grid’s innate rectilinear lines. The prism’s steeper slope is keyed to P-R landscaping berms and farm field furrows and as these attune to the abode’s alignment, their maximum slopes pose the fusing angle to the universal average of the default CBA embanking slope. D-grid berms use the prism’s shallower slope for broader landscaping and orchard designs – and to complete a flattening progression away from the abode.
Advanced Approaches – 4
Although the quantized shapes of waveforms are small in number, scaling and terracing allow much flexibility and variation in ground design. Another particularly important consideration is how to merge the highly specified wave with random terrain. The easiest and most elegant approach entails a clean interface that sets off the virtues of each such as a straight or rounded vertical walls. Thus far, examples have been convex in nature but concave contouring is just as valid.
Basically, a concave wave is formed by spinning it about its trough rather than its crest to allow a way to embank inside corners of courtyards (or abodes); or form berms in T, U, or L shaped configurations. These may be a feature of “outside rooms” and may sprout – along with desired flora – trellis supporting posts while their max slope contours define bench seating cutouts. Finally, an alternative water-draining “flat” is keyed to the small angle spun to make earth’s cross-section a perfect circle.
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