Sublimity of Structure:
Bucky Fuller’s Cuboctahedron
By Hyatt Carter
Just what is reality, and what makes for a good model of reality? One model that offers both clarity and simplicity and, upon reflection, turns out to be most satisfying, was used by Buckminster Fuller in one public lecture after another as he toured cities all over the world speaking to audiences about his new ideas.
And what is this model of reality?
The common overhand knot, made by turning a rope in two interlocking circles, thereby forming two lobes that, if pulled taut, curl up snug, one against the other.
Is the rope the knot? By no means. Imagine three ropes made, respectively, of cotton, hemp, and silk. Splice them together, tie a loose knot, and slide the three ropes through the knot, one after the other. The materials—cotton, hemp, and silk—serve only to make the knot visible. The knot itself is not material. It is, as Bucky1 tells us, a self-interfering pattern.
Self-interfering? In the illustration above, in the center picture, note how the two lobes, one made with dotted lines, “interfere” with each other to form the knot. Pull the knot snug, with all your strength, and it will resist exertions to be pulled any tighter.
The knot is a patterned integrity: a whole with dynamic balance of two vector forces—one directed in; the other, out.
Other wholes, such as atoms, molecules, and living cells, are knottings of energy. What is it that holds such entities together—that is, what holds them together, and at the same time apart, in dynamic and elegant unity?
Just as in the rope knot, two complementary forces dance in measure to make them a patterned integrity, a self-interfering pattern. Compressive forces, pushing in, mirror the tensile forces, pulling out. The same anew for planet Earth as she orbits round the sun.
And what about us—the human knots—into, through, and out of which pass, annually, tons of food, water, and air, like so many lengths of rope, to make us visible or, should we say, corporeal? But what are we? Not a substance, surely, and surely not a thing. In a process world, as in Buddhism, there are no things.
Ernest Fenollosa: “Things are cross-sections cut through actions, snapshots.” And therefore static in a world where the reel rolls on . . .
Then what is truly real? A reiterative self-interfering pattern . . . woven with naught whatsoever except the weave itself. Sunyata: emptiness.
What knots we are!
Knot So Simple
There is another knot, and one more elegant, that shines with what Bucky calls tensegrity.
Tensegrity stands for “tensional integrity” and refers to a balance between the tensile and compressive components that form structures such as the cuboctahedron, pictured below.
A Knot Called Cuboctahedron
Bucky calls it a Vector Equilibrium. Once you understand the structure, it’s easy to see why. First, all the lines, both internal and external, are of equal length. On the surface, triangles alternate with squares. Internally, an emerging pattern can be glimpsed wherein tetrahedra alternate with octahedra, thus expanding the motif of three and four.2
Notice that twelve vectors radiate out from the central point to touch each of the twelve vertices of the figure.3 The restraining rings of four hexagons crisscross its perimeter, the rings so arranged that two intersect at each vertex, weaving a tensile web
Imagine: energy radiates out from the central point, along each vector, and is countered, at each vertex, by the network of tensile forms on the surface, constraining in, so that a dynamic equilibrium is achieved. Like an inflated balloon, the figure models a contained explosion. It is a self-interfering pattern. And, since tensile and compressive forces have been equilibrated, it is quintessentially stable, but not, like the Platonic forms, static.4 Like an atom, or a molecule, which it models truly, it sizzles with energy. It is, after all, a contained explosion.
Hence, Vector Equilibrium.
1. Bucky: short for Buckminster.
My first acquaintance with Bucky Fuller came through Hugh Kenner’s magisterial book, The Pound Era, recommended to me by Professor James Watson when I was a student in his 20th-Century American Literature class at the University of Tulsa. This essay draws heavily on that book. The rope illustration appears on page 145.
2. I say emerging pattern because the Vector Equilibrium is the cell, the basic unit, that forms the lattice known as the Octet Truss, an amazingly strong structure that can bear massive loads. As Hugh Kenner points out:
“Any node in the Octet Truss lattice is the center of a vector equilibrium: a point from which twelve vectors radiate into rings of restraint. That’s where the Octet Truss gets its great strength: every stress is dissipated twelve ways, and caught in those rings.”
For his idea of the Octet Truss, Bucky was awarded U. S. Patent # 2,986,241.
Place a heavy weight on a cube and it is likely to collapse. Place the same weight, or even more massive weight, on a Vector Equilibrium and it contracts symmetrically, smoothly, as the load is evenly distributed throughout the tensile web of the structure.
With many VE’s synergistically linked together in Bucky’s 60-degree space grid, the Octet Truss, the weight is even more finely distributed. The Octet Truss has massive, almost redundant, structural integrity.
3. These 12 vectors are not part of the figure but are inserted to explain its dynamics.
The cuboctahedron, one of the Archimedean Solids, is a structure with 14 facets, 24 edges, and 12 vertices. But seeing it only as a solid reveals only half the story, and not even the more interesting part. Kenner again:
“If you think of the cuboctahedron as solid, you concentrate on its surface, where the irregularity strikes your eye, and dismiss its interior as a featureless putty. So you won’t reflect that it has a natural center, and that the vectors radiating from the center are exactly equal to the vectors that bound the faces. No other structure in space can make this claim.” [Emphasis mine]
And so, in this figure: 36 lines of equal length, suggesting a balancing of forces.
4. For Bucky, even a simple triangle is no idle Platonic form, but an energetic triangle, made of six events—three compressive sides and three tensional angles—with each side hard at work stabilizing (compressing) the angle actively tensed opposite it.
The same can be said, and even more so, for a robustly stable structure that is the three-dimensional equivalent of a triangle—the tetrahedron:
The tetrahedron is the form, or structure, of the posture of zazen, or seated meditation. This becomes obvious if, in the following schematic, you imagine the hands placed on the knees with arms straight.
The form of zazen, the lotus posture, will be the subject of Part Three in my series on Sublimity of Structure. Throughout his life, Dogen was steadfast in his conviction, and in his experience, that zazen itself is enlightenment, that practice and enlightenment are one.
Form itself is emptiness,
Emptiness itself is form.
Quotations in Notes 2 and 3 are from: Bucky: A Guided Tour of Buckminster Fuller by Hugh Kenner.