The Rolling Transport series of posts concluded with 2 approaches to accommodating wheeled artifacts architecturally. Although there is nothing really lacking in the usefulness of these simple configurations – IMO they serve their purpose very well – the wheel slot and the wheel port annexation are only 2-dimensional.

To begin the series of posts on Polytechnic Integration, a deeper connection between template-guided transporter and CBS architectural forms is sought by once again looking to the macrocosmic wheel. After longitudinally aligning its central hexagonal edges via primary rotation, the great wheel undergoes secondary rotation such that any one of its outermost edges is oriented horizontally at a specified latitude.

Zooming in on the spot with the wheel’s innate microcosmic representative in attendance (below), perspective is turned to a polar view with edges of plane types sloping from each side of the horizontal edge identified.

Next, the wheel’s natural halves are separated and – with the triangularly sloped side held in place – the sloping square side is rotated 60° such that a sloping triangle mirrors that of the fixed side in the same hexagonal shift that formed the basis of the transport template.

Then focus sharpens on the matched triangles which are detached from the microcosmic wheel and juxtaposed against the CBS home’s latitude dependent roof.

To make the fit, the angle of the sloping triangles is adjusted such that the outer points contact the roof/wall juncture and the central ridge joining the triangles maintains a horizontal bearing.

The precise angle of adjustment (Φ) is of course related to the slope of the CBS roof (Δ)which in turn is either equal to the latitude (Θ) or complement (90° – Θ), and is given by the *fusion formula*:

Φ = ArcSine [ (√3/3) TanΔ ]

In temperate latitudes of both north and south hemispheres, both polar and equator-facing roofs are receptive to these fusions. Outside these latitudes the fusion is can only be implemented on one roof.

Such latitudinal variation makes “triangular wings” an apt term for the mirrored pair. Spreading the wings to their extreme forms the rudiments of a hexagonal pattern viewed from above, while completely folded, they pose one triangle from either profile.

With the tri-wings fitted to the (rectangular) roof, the overhanging portion is clipped flush with the wall to leave 2 half triangles while appearing as nothing more than a highly specified cross gable.

As such the gable’s slope gives indication of latitude from a polar perspective (with the fusion formula solved for such) to round out expressions of the celestial cube projections from all directions viewable from the ground.

Together the clipped triangular wing halves combined are of course equal to one triangle – the simplest expression of the planar cuboda’s wheel orientation. Considerable time and thought went into this approach with several previous approaches rejected as lame and I wasn’t exactly thrilled by this solution. Why? Because it wasn’t unique or novel. But as its sensibility quietly grew on me, I came to wonder if perhaps the advent of the cross gable was an instance where the code’s fundamentals were being followed in a groping way.

Whereas architectural annexations and wheel slots only involve walls, this fusion involves both the co-cube projection *and* the added dimension manifested by the roof. Neutralizing the macrocosmic wheel via symmetry of the h-shift bestows upon the transporter an apt place of rest, while tension created by the difference between template and adjusted angles can be viewed as building potential energy to charge the transporter for its intended work.