Wheel Extrapolations

As rudiments of shelter and land transport have been individually established and integrated to each other as well as to the ground supporting them, the dynamic bodal wheel and its neutralized manifestation here frame the design of rotating fluid dynamic constructs; the marine, air, and spacecraft powered by them; infrastructural support; and standalone architectural alternatives.

Part VI adapts previous general applications to more specialized ones, with simple examples depicted in the gallery and detailed treatment of them found in the 13-page PDF. This page of introduction is divided into 5 sections, with underlined words and phrases having glossary entries.

Wheel-based Shelter – 1

As the bodal prism finds expression in ground waveforms, the likewise grid-attuned macrocosmic wheel serves to guide alternative architectural schemes. However, regardless of the grid type hosting the building, the pattern provided by the celestial cube projection guides the design of that building’s walls, floors, ceilings, etc.


The big earth-centered wheel – upon being neutralized, made symmetric, and aligned to the polar-rotational grid’s longitudinal direction – guides the pitch and pattern of roofs from its matched squares. In such a scheme, appendages to north and south walls are topped by cube-based abode roof sections. With diamond grid structure roofs, the wheel’s matched triangles determine pitch and pattern.


These hip style roofs are geometrically conducive to lateral or vertical extensions – or clustering for commercial, institutional, industrial, and agricultural applications. In either grid type, the building’s underlying wheel geometry imbues it with a restrained dynamism while underscoring that grid’s distinguishing wave contours.

 Path – 2

The neutralized macrocosmic wheel – or more precisely its microcosmic representative – also supplies guidance for that which the wheel rolls upon: path. Such application follows from the correspondence between bodal wheel and edge-up prism geometries, and how the mirroring of their triangular stability affords strength against deformation to minimize rolling friction. Furthermore, alternation of these geometries’ asymmetries poses a periodic picture of dynamic resonance.


Application of path geometry ranges from symbolic to actual contouring to structural explicitness. For example, road and highway side slopes, traffic islands, or  paralleling berms that frame path are guided by the edge-up prism, while farm field furrows are shaped to actually accommodate the wheels of rolling machinery. The most explicit path expression is found in bridge design utilizing all path structure elements, integration with other apt bode orientions, and bode-specified parabolas.

Non-rolling Transporters – 3

If bridges are not feasible in surmounting gaps, the free microcosmic bodal wheel-based transport template may readily be applied to marine vessel and aircraft designs. Depending on speed and altitude, design of the latter may heavily rely on the template’s innate motion-aligned cylindrical forms. Otherwise, a wholistic angle of attack may readily be chiseled from the template’s pattern which may also totally envelope the template’s central hexagonal expansion geometry.


Finally, the template’s matched (top or bottom) triangular planes supply the pattern for general wing design which manifests on the airfoil cross-section along with bode derived parabolic or waveforms. For watercraft, a keel naturally extends downward from the template’s central, vertically-aligned plane. The biggest concern in adapting the template to boat and ship design is sealing the space between the exposed HXP-guided decks, superstructures, and holds – and the hull’s bode pattern planes.

Bodal Turbines – 4

img_0087To power these non-rolling transporters, the bodal wheel is once again engaged, with the bode’s internal planes brought heavily into play to guide propeller design. From such, a variable (zero to very high) pitch propeller is easily sculpted. This and other design approaches may utilize the rotation angles necessary to re-orient the wheel’s default direction of motion with the template to that of the propulsion axis. On the flip side of fluid dynamic bodal turbine applications, wind and water is harnessed to generate electricity in dams or vertical axis wind generators.

The Disc Orientation – 5

In the positioning alternatives of driven turbines, artifacts in which the bode’s central bisecting plane parallels the surface of travel are evoked. Relevant surfaces include hydro-spheric and atmospheric boundaries, or continuous iso-gravitational potentials. In this latter circumstance, the satellite poses the simplest application of the disc-oriented bodal wheel.


To imbue the disc with direction for non-shuttling air, water, and space craft, a bow like structure is formed by minimally appending appropriate polyhedra. In doing so, a stern square is distinguished much as the one pair of equatorial squares is with the geocentric cuboda. Whilst the celestial cube-based abode is fixed to earth, the direction-imbued disc poses a freely moving alternative.

Wheel Extrapolations PDF

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