RB Fuller Angles

For some older readers, the earth-centered and coaxially-aligned bode maight evoke the Dymaxion World Map Projections devised by R Buckminster Fuller in the 1940s. Indeed, there is a connection and it begins with my first exposure to Fuller’s world by way of the Whole Earth Catalog back in the 70s.

At that time, I had just purchased a lot from what I earned on my first overseas diving assignment. As I mused on what to build on it, I entertained the possibility of a geodesic dome. Eventually however, after hours upon hours of adapting floor plans to the icosahedral shape on paper, I soured on it and switched my focus to the other form Fuller promulgated – the cuboctahedron.

Around about this time, while onshore for some R and R, I found myself waiting for an elevator at a higher level of a Singapore hotel. When it arrived, stepping out crisply dressed was non other than Mr. Fuller himself. For one brief moment, the light bulb that seemed to superimpose his head turned to regard me through thick bottle glasses with a look that instantly diminished the swashbuckling persona I cultivated to one of a bug under a microscope. Before it dawned on me that this was the man whose work I had been trying to engage, Fuller had strode purposefully off and was long gone.

Later, as my interest in the cuboctahedron grew, I noticed that as much as Fuller extolled the form’s virtues, his application of it was limited. He did use it in early versions of his world map and the octet truss, but not architecturally. For that he employed the icosahedron.

Consequently, I sensed virgin ground in the cuboctahedron, and as my interest mounted with the possibilities, I came to guess that the reason Fuller didn’t apply it more was due to some sort of perceived conflict between the implications of abstract forms. Yet, in expressing disdain for rectilinearity, the all-triangle icosahedron he based his world maps and domes on has for its most minimal expression 3 interlocking rectangles whose characteristics, planes that essentially divide more than organize or enrich space at its core.

Rectangular Icosahedron

In his earlier world map projections using the cuboctahedron, Fuller seemed to be trying to figure out how to orient the form with earth’s polar axis, pegging it to a square or a triangle. In his archives* however, he expresses regard for the virtue of aligning the planet and the cuboctahedron coaxially, most notably for navigational purposes. Perhaps he went no further with the idea because to do so would have conformed to established ways and conflicted with the novelty of ideas getting so much attention. At any rate, this appears as close as the idea of the geocentric cuboda would get to its conceptual grandparent.

Aside from choice of form and how to orient it, the basic difference between the geocentric cuboda and Fuller’s maps is that with the latter earth is projected onto the encasing polyhedral form while the latter projects its geometry onto the earth. Another key difference is that the maps are fixed to earth in a particular way which I imagine posed some real priority headaches. Conversely, the geocentric cuboda is characterized by a defined method whereby its geometric features may be located anywhere, equally and universally.

After the novelty wore off, the maps were found to be of even less practical value than geodesic domes. Although they technically succeeded in lessening distortion (relative to the Mercator Projection), those distortions were enormously complicated to deal with.

But even if the maps were ultimately not practical and his cuboctahedron-based octet truss actually works against his most noble ideas (think highrise cranes and big box flat roof structures), Bucky’s   applications were successful in getting a lot of attention and thus his ideas provoked much thought in new directions. For that I owe Bucky, and strive to pay it forward with my own answer to his call for comprehensive design.

* (edited by Thomas T.K. Zung) Buckminster Fuller: Anthology for a New Millennium, Chapter 19 – “The Mind of Buckminster Fuller (from Synergetics Dictionary)”, (St. Martins Press, January 2001) p.  338

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