CBS Roof Options

The nature of celestial cube-based shelter together with the cubodal wheel fusion poses the potential for 2 cross gables of differing slopes for any such house built in temperate zones between 30° and 60° (except at 45° where both gables slope at about 35°).

Temperate Latitude Fusion Variability

From that middle latitude, the difference between the gables increases – along with the CBS host roofs – until at 60° the polar gable reaches 90° to essentially vanish and the 30° gable settles at about 19° according to the fusion formula.

Φ = ArcSine [ (√3/3) TanΔ ]

Beyond 30° and 60° latitudes – in subtropical, tropical, arctic and subarctic realms – only one CBS roof is receptive to the fused gables – except at the poles and equator where any fusion whatsoever is precluded.

Such restricted variance coupled with the varied directions  of road access gives transporter accommodation the potential for being a convoluted undertaking. Fortunately, however, there are options available that are attuned to code geometry and philosophy.

The simplest option pertains to the steeper fused gables – the steeper the more applicable. In this option the 2 half wings  are separated such that the ridge becomes a 2-dimensional flat plane. In fusing to the roof’s prime cube projection according to the fusion formula, such a plane will be flat relative to the local horizontal shown by a level. To attain water drainage this plane can be tilted slightly according to the co-cube projection correction.

CBS Cross Gable Horizontal Plane Extension

At this point, it should be stated that the steeper fused gable need not be for transporter housing. The gable can also be used for vents, windows, or bracing for vertical sun-blocking planes. If separated semi spherical skylights atop the resulting flat roofs are perfectly consistent with code geometry.

Another option applies to both shallow and steep gables and is a bit more complex but offers interesting configurations. Hybrid transporter housing combines the annexation approach with one gable slope.

CBS Hybrid Roof Fusion-Annexation

With the hybrid roof, the annexation extends horizontally beyond the confines of the CBS roof such that its ridge is matched by that of the half gable. This configuration of course poses a corner approach to transporter housing.

The hybrid roof enriches the base CBS style with a combination of universal and variable elements. But because a certain complexity is also introduced, the code lays down rules for their implementation to avoid clutter and confusion.

1) an annexation can only extend past one CBS roof (north or south) so as not to obscure or undermine CBS expression of the juxtaposed celestial cube projections.

Wheel Housing Roof Rules

To construct hybrids using both gable angles (in temperate latitudes) they must be done separately on opposing (east and west corners).

2) separate (full) fused gables and annexations are not allowed on the same structure unless the 2 modes are informed by a hybrid roof.

Hyrid Fusion Rules

With a particular sloped hybrid, either the annexation or the corresponding fusion or both may be constructed.

3) only full fused gables are allowed on mirror roofs, i.e., no annexations or hybrids. The reason for this is to avoid obscuring expression of the CBS celestially projected cubes. Mirror roofs already provide sufficient flexibility.

Mirror Roof Fusion Rules

Such fusions are exempt from the rule requiring hybrids to be present for them and separate annexations on the same structure. If a hybrid is used, it must not be on the same side as the mirror roof to avoid confusing or obscuring CBS expression.

Again, the options and their rules are intended to afford variegated flexibility for particular circumstances while retaining intra-latitude identity and inter-latitude code integrity; and they lend the code’s CBS style – otherwise known as Humble Cosmic Architecture – more well rounded roundedness and pose a richer gem without diminishing its unique essence.



Posted in Code Application, Cube-based Shelter, Philosophic Bases, Polytechnic Integration, Rolling Transport | Leave a comment

Dream Machine

For the last several months, I have been hunting for a new bicycle – one to replace a very worn out and decrepit Jamis Earth Cruiser.

Criteria for my perfect bike are comfort, ease of operation, low maintenance, and general practicality with the ability to carry loads on any kind of surface over any kind of terrain in any kind of weather. Weight and speed are not big issues with me, but I am looking to go a little faster, which for me would be cruising comfortably at about 15 mph as compared to 12 mph with the Shimano 8-speed coaster brake-equipped Jamis.

Another major criterion is a frame design consistent with the geometry of GDCode’s transport template, or at least as close as possible. With regard to this factor, the first bike to catch my attention was the one used by the Bixi bicycle sharing system which is deployed in a growing number of big cities. After much digging I learned these bikes were not for individual purchase, but during my search I obtained a link from a forum to a bike that was claimed to be similar. In pursuing it, my first impression of the Biria step thru was of a huge black glistening metal arachnid which I immediately dismissed.

In the meanwhile, I had another Jamis in mind, one spotted on their website. In general the “Hudson” was what I was looking for – a leaner faster cross between a cruiser and a hybrid comfort bike. However, special ordering was required from a dealer who seemed averse to doing so. Aside from this problem, the cruiser I had had given me much grief over 5 years. But it was the devil I knew, and realized that succeeding the steel Pan Am made by Caloi (which discontinued North American operations) was a hard act to follow. At least the Jamis got me through years of long distance commuting and supported mostly successful experiments with a hub dynamo and an AA /AAA USB battery charger.

As I pondered the plusses and minuses of another Jamis, I stumbled on a real life Biria in a bike shop, where it looked much better in white, so good I requested a test ride. I was pleasantly surprised at how nice it rode and despite a slightly odd feel to the sharply swept back handlebars, the bike became a candidate.

After more searching, the Electra Townie was the only other bike I seriously came to consider. There was a shiny copper specimen at one bike shop that countered doubts I had about it being too laid back and therefore slower than a conventional cruiser.

Compare to the roundedness of Earth Cruiser and the straigness of the Caloi before it, the 3 candidates exhibited a combination of  straight and curvature. To help my decision, I downloaded photos of each bike and superimposed lines angled according to those characterizing the transport template. Beyond horizontal and vertical, those lines slope both ways at 30° and 60° angles. For fun I also marked 45° lines.

Jamis Hudson - Template Geometry Comparison

As much as I liked color, simple elegance, 3-arm chain ring, and dolphin-like hump of the Jamis Hudson (above), it was a little off on scant geometric matchups.

Electra Townie - Template Geometry Comparison

The Townie was a little closer with more matchups, enough to have me finally taking a test ride which proved the semi-recumbent posture not as weird as anticipated.

The Biria was the most attuned and it was also available in a color that was close to that of the most beautiful car I have ever seen – a retro Thunderbird circa 2004-06.

Biria Easy Boarding - Template Geometry Comparison

As the color matched the car,  so the bike’s step through design evoked stepping into a car – instead of lifting your leg like a dog at a fire hydrant – a sensible approach that I think will help make the bike more acceptable as a standard mode of transportation.

To me, the unconventional arc of the bottom piece is a bit reminiscent of the bulb on modern ship design plowing easily through the water – or skimming over the air like a magic carpet. I probably won’t reach the 15 mph goal until upgrading to more gears from the 3-speed coaster brake, but as pleasant as the ride is now I am in no hurry.


Posted in Code Application, Code History, Rolling Transport | Leave a comment

Full Wheel/House Fusion

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.macrocosmic wheel-house fusion

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.

hexagonal shift of microcosmic wheel

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.

Roof Fusion of Cubodal Wheel

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.

Cross Gable Wheel Port

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.


Posted in Code Application, Code History, Cube-based Shelter, Derivations, Polytechnic Integration, Rolling Transport | Leave a comment

Polytechnic Intro

The middle part of Geocentric Design Code’s 7 parts can definitely be the most dry, complex, and out of range for all but the very motivated, but, it is also necessary. To ease the pain – some air for Part IV’s title: Polytechnic Integration is the incorporation of polytechnic functionalities via integrated polyhedral re-orientations.

Polyhedral in this context refers to the cuboda (cuboctahedron) and its components (tetrahedra and octahedra), and the cube (hexahedron). By definition, “polytechnic” pertains to a variety of technical arts and applied sciences. The poly- prefixed words are linked by the requirement that functional constructs designed must effectively respond to natural law (physics), and by the simplified geometric representation of that law.

The word “polytechnic” also has special significance for the place of my birth and upbringing in the San Luis Obispo area of California. In my time Cal Poly has always hovered over the region as the dominant institution, economic force, and transient population, but I had little appreciation for the college until attending a “Poly Royal” – the school’s annual open house of yesteryear, while a teen. It was then that the meaning of “polytechnic” was driven home with exhibits and projects ranging from architectural to agricultural to just about every engineering field. After this one exposure opened my eyes to what the greater world was doing, I sometimes felt as if I was absorbing polytechnic  creativity from the air.

A half century later, the notion of a polytechnic spectrum called to a burgeoning design code upon the fusion of transporter and architectural forms, specifically a full fusion as opposed to the superficial integration of the methods described in recent posts. Delving into the deeper (3D) fusion engaged geometric relationships that I found could reasonably be applied to other connections.

In reviewing the existing Part IV’s 10 pages (of the 70-page PDF) however, I found the presentation of integrating ideas and applications so unintelligible Part IV might as well be titled Polytechnic Entanglement; and If accessible to hard core interest, it is surely devoid of any inspirational merit. So preparing for an expanded revision similar to what the first 3 parts have undergone, I have wrestled with how to make the material more easily digestible.

Ever striving for a linear approach where each concept builds logically upon what has preceded it, I have found that Part IV is not so simply organized because it theoretically could start with any one of a handful of basic concepts. In fact, I have even entertained the idea of switching Part IV and Ground Design because treatment of the latter doesn’t absolutely require the concepts of the former.

There are compelling resons for making the switch, but I have decided the overall flow would best be served by keeping the same order. What needs changing is the order within the subjest’s material. What I am going to start out trying is the easy-to-picture (and apply) fusion of shelter and transport, and then describe the underlying geometry afterwards which can then proceed to be applied in other key practical situations.

In the most plain terms, what amounts to a triangle-to- (cube) square fusion will turn, and ultimately proceed, to the opposite process where the square is fused into the triangle. By so doing, applicability of the triangular transport template will be expanded to guide sea and air transporters, as well as working mobile artifacts such as agricultural machinery, fishing boats, and exploration spacecraft.

Exactly how these will take shape awaits Part VI, but to prepare for them Polytechnic Integration will mostly be geometric gymnastics with just enough application examples to make it real. In embarking on this expansion I don’t foresee any new math beyond the simple trig expressions stated in the existing version, but I can’t truly predict what will come to light diving deeper into the applicability of code geometry in the next few months.

What gives Part IV its character and demands special treatment for it is revealed in linking intermediaries developed which manifest the difference between centuries’ long use of the cube for artifact design and addition of the more physically attuned cuboda straddling and orienting both the cube and the sphere. In the end, appreciation for the universal link of the latter will make the earth ripe for such interpretation in Part V Ground Design.

Posted in Code History, Polytechnic Integration | Leave a comment