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Since the dawn of humanity aboard Spaceship Earth, nature has been our principal teacher.
Her technology is clearly superior to ours, and that has not changed, although our insights into
her inner workings have most definitely improved.
"Tension and compression always-only co-exist" says Bucky Fuller. He talks about rope, how it
compresses at 90 degrees to its axis of stretching, and about barrels of wine and/or whiskey, and
how their staves are held in compression, against the outward pressure of their contents, by
bands of tensed steel. In a star, the radiation is pushing outward, compressively exploding into
the surrounding environment, while the tension of gravity allows it to stay ball shaped.
Early humans would have learned from animal skins and internals, from leather, from antler,
from sinew, bone and gut. Shellfish provide lessons in both tension and compression. Woven
materials may be used to suspend, as when hammocks are hung to hold and rock babies.
Skins were turned into canteens, tensile containers for liquids or powders.
The vegetable world offers lessons with vines. Wood will bend and compress without
snapping, as do trees in a wind storm.
The mineral world would seem mostly compressive, but then is ingested to play a vital chemical
role in the pneumatic, stretchable world of the biological forms. We discovered this later, along
with metal wires and alloys.
Categorizing energetic deployments as compressive and tensile takes insight and practice.
Engineers need to feel it in their bones. A large dam holds back a body of water, which courses
through pipes to the turbines below. The dynamos powerfully resist turning, have behind them
the heavy lifting needs of an entire city, complete with tram lines and air conditioning. The
dammed river provides enough torque to keep the blades turning, not at a really high speed, but
steadily. The wires from the generators are called high tension lines. The electricity within
these metal wires alters direction many times a second as the spinning magnets jiggle their
electrons back and forth.
When it came to early architecture, humans had two entirely different environments to contend
with: the surface of the land, and the surface of the sea. Travel by sea may have started much
earlier than some historians allow (most will accept it back to 8000 BC). Whether or not this is
so, tension gets more emphasis at sea, especially where rope and sails are concerned,
whereas on land one is rewarded for heavy masonry. That which would be worthless as a
floatable hull, is on land considered a prized fortress or palace, perhaps a temple or pyramid.
Buildings on land tended to weigh a lot and thereby connote permanence.
Not so long ago, humans took to the air in a big way. A dirigible or hot air balloon consisted of
fabric, a mostly tensile material. Fixed wing aircraft proved much faster and controllable as they
sliced through the air. Submarines developed around the same time, then spacecraft. One
might consider these five key types of operating environment (under water, the water surface,
land, air over land or water, outer space) each with many subtypes.
The principles needed to create life support in each of these environments evoke their own
architectures. Learning from nature is a first step in each one and many next steps as well.
Humans learn kinesthetically among other ways. Each environment requires its characteristic
physical abilities. Sailors need sea legs. Land dwellers may need climbing skills.
As humans became more adept, they learned to demand less adaptation in some cases. One
could become a passenger on a ship or airplane without any training in sailing or flying, nor
would one's physical experience seem especially extraordinary. The ship would be gigantic and
hardly rock in calm seas. The airplane might go through bumpy patches, yet you could eat
dinner and watch TV.
The blending of air and sea environments might be considered the genesis of aerospace. A
question facing early 21st century humanity is whether to take an aerospace approach to the
land dwellers. Since most of us dwell on land at least some of the time, this could be to our
advantage. Various mass produced hulls have been proposed and prototyped. Our agreeing
on a single aesthetic for future shelter solutions is probably not in the cards, a good outcome, as
diversity begets adaptability. Not everyone cares to live in a yurt, no matter how up to date and
geodesic dome like.
Among the land dwellers, a paradigm building strategy consists of piling stones on stones. If
the stones are heavy enough, then the inward pull of gravity is sufficient to keep them aligned
atop one another, even through minor earthquakes. In later times, before reinforced concrete,
bricks and mortar entered the picture. The brick-and-mortar medium, if we may call it a
medium, is omni-extensible, because rectilinear prisms, golden cuboids, simple XYZ cubes, are
known to fill space. Just about everyone can imagine a quasi-infinite "brick ocean" from which
almost any shape may be made, simply by subtracting enough bricks (or call them voxels, the
three dimensional equivalent of pixels).
As tension became more important on land (the maritime influence) through aerospace in some
cases (the Seattle Space Needle for example) the bricks began to figuratively separate and float
freely from one another. In place of mortar, a more tensile weaving would occur, though without
losing all compressive properties. The Flextegrity project was and is a clear manifestation of
this development in an almost literal sense. More metaphorically, the ratio of tension to
compression was and is increasing, as symbolized by the widening inter-distance between the
bricks.
The Golden Gate Bridge in San Francisco stands as a testament to what tension might
accomplish.
Bucky Fuller's hanging buildings, sometimes multi-story, at least in design, were likewise about
using materials in tension, a more-with-less, lighter-weight strategy. Entire towers might be
delivered by dirigible in his vision.
The 19th and 20th centuries brought a new appreciation for geometry in nature, thanks to the
earlier invention of the microscope, photography, and better drawing techniques. The world of
the very small, observable yet not directly habitable by full scale human beings, proved to be an
almost Platonic realm in the perfection of its geometry. That nature was still somewhat skewed
and aberrational vis-à-vis the pure Platonic forms endearingly revealed her passion for
individuality, which we recognize within ourselves. No one is frozen in the matrix, because that
"matrix" does not exist as a compressive physical barrier or prison. The principles keep us in
tow, lagging behind at various rates.
Explorations of the mineral realm brought us into closer contact with the principles behind rigid
geometries. The topic of "sphere packing" began to emerge in the collective mathematical
consciousness, along with Bravais lattices and space-filling polyhedra.
Johannes Kepler, far ahead of his time, was already studying rhombic dodecahedra in a cubic
close packing (CCP), and Penrose tiles (anachronistically speaking) in the 1600s. These
understandings later bloomed in the 1900s, at a time when geometry had already gone hyper-
dimensional. Hypertext would come next.
As the compression-oriented land dwellers became more informed by the principles of tensile
design, their bricks not only grew further apart, but rearranged themselves in a more 60-degree-
based, less 90-degree-based array. The kites of Alexander Graham Bell heralded this sea
change. These kite patterns later reoccurred in the form of the octet truss, a building strategy
patented by the same person who patented the geodesic dome, Bucky Fuller. Mathematicians
knew they were looking at the same face-centered cubic lattice each time, a kind of home base
for crystallographers as well. The mineral and atomic worlds had taken us deeply into the
Platonic realm and of the five Platonics the simplest is the tetrahedron not the cube.
"Remembering the importance of the tetrahedron" might be considered a theme of this era,
beginning with the chemical studies of Linus Pauling and ending with the discovery of
buckminsterfullerene and nano-tubules, as well as of quasi-crystalline structures and the
icosahedral nature of the virus. The tetrahedron is implicit even where the mosaic consists of
mostly hexagons, a few pentagons. Its structural stability and all 60-degree surface angles are
iconic, like a logo or trademark.
The importance of triangles to structural stability was realized by the ancients. The Native
American tepee is a clear instance of an omni-triangulated structure. The poles are bound at
the apex and fan out to create a series of triangular facets. High winds will not easily knock it
over. The skins wrapping the skeleton keep the heat in, the rain out. With just three poles this
would be an unusual tepee, yet would form an enclosure. This is our "minimum tent" and is
therefore a better symbol for a primitive shelter than any square-walled hut. The latter is not
minimal, nor is it stable without the triangulating effects of bracing struts, or simply mud.
Tetrahedral tepees are more tensile than cubic huts, and therefore serve as an icon for
aerospace know-how, much of which centers in the Pacific Northwest.
How might one join four bricks in a tetrahedral array? One might learn in school that Aristotle
was wrong: regular tetrahedra do not fill space. Our tetrahedral array of four bricks will need
complementation. Sometimes four bricks meet, defining a tetrahedral void; other times six
meet, surrounding a void of another shape, an octahedron. Six lines of inter-relationship define
the three intersecting squares of the regular octahedron. Tetrahedra and octahedra fill space in
complement.
In a quasi-infinite "Brick Ocean" of this design, every brick will have twelve nearest neighbors,
each one equidistant. If the array continues in every direction, everywhere the same, much as
an ocean of cubes might, then this pattern of four-meeting and six-meeting will continue. The
number of meetings-of-four will outnumber the meetings-of-six by a ratio of 2:1. We have twice
as many tetrahedra as octahedra. Crystallographers might call this a Barlow packing, if made of
kissing spheres instead of bricks. These could be ghostly spherical domains, inter-tangent only
in principle, anchored to their brick nuclei, which add physical reality to this picture. XYZ, the
coordinate system, is likewise ghostly in the sense of imaginary, weightless, a reference frame
rather than a feature of the physical environment.
In the Flextegrity design, our bricks have changed their form, from unstable hut shapes, to a
more space age icosahedral shape. Icosahedra are ultra-stable yet share some of the cube's
symmetry. Three golden rectangles, mutually perpendicular, pick out sets of six from the
icosahedron's thirty edges. Six is half the number of neighbors each icosahedron expects.
Two grips to each of six edges will be the ties to one's neighbors. Six pairs of competing grips
will end up holding each hub stationary and at rest. The griping arms, possibly springs, do not
pull in a radial fashion, asking the icosahedron to expand outward. They pull laterally, applying
rotational torque, but with their forces counter-balanced.
When an external load is applied, each hub communicates stress along the segments
connecting to it. The external force is distributed to nearest neighbors, and so on to their
nearest neighbors. Given nature sees fit to operate this way, especially in the mineral kingdom,
it's no wonder that Flextegrity proves to be a strong, robust material. Stand or jump on the
plastic prototype. She does not break, at least not easily.
The specific substance is immaterial from the standpoint of the geometry, which is to say one's
choice of substance is left to the individual architect-engineer. Plastic injection molding has
provided an initial five versions, suitable for experimentation.
Like ordinary bricks and mortar, Flextegrity is omni-extensible, forms a "brick ocean" of twelve
bricks around one. In place of bricks, we sometimes have icosahedra, stable and strong. In
place of mortar, we have a weaving pattern, though not in the style of the octet truss, and not in
the style of the tensegrity sculptures.
True, the bricks form the same crystal pattern as the Alexander Graham Bell kites represent, the
face-centered cubic lattice (FCC), equivalently the CCP in the realm of sphere packing.
True, the hubs are primarily compressive, and may be considered floating in the sense of not
touching one another. "Floating compression" is sometimes used as a synonym for "tensegrity"
by Kenneth Snelson, its proud father (Bucky Fuller was more of a godfather).
However, in both cases we find significant differences. By comparing and contrasting
Flextegrity with these other patented inventions, we might come to understand it better.
Returning to Johannes Kepler, ahead of his time, we remember that rhombic dodecahedra are
space-fillers. Place a ghostly sphere in each one, nesting perfectly to just touch each of twelve
diamond face centers. When any two rhombic dodecahedra pack together, face to face, their
contained spheres will form a pin joint or kissing point. We do not need "faces" at all, as the
rhombic dodecahedra may be an imaginary grid, as ghostly as the spheres themselves, purely
conceptual.
A straight line from each nucleus to a neighboring nucleus will pass through a kissing point
perpendicular to the diamond facet. Twelve such segments to the vertices of a cuboctahedron
(the dual of the rhombic dodecahedron) provide the inter-nuclear transit tubes of the octet truss
matrix. Flextegrity, however, does not run its transit tubes in this way.
Looking up from the bottom icosahedral brick (hub) in a meeting-of-six, one sees a counterpart
hub directly overhead. Surrounding this clear span atrium to the roof top is a mezzanine of four
additional hubs, arranged in a square. The bottom icosahedral hub presents an edge, a beam,
along its vertically facing apex. To this beam, two grips attach, stretching laterally to each side
though slightly upward, where they grip two of the four mezzanine neighbors, with edges along
their bottoms. The other two mezzanine neighbors are met with vertically and from the bottom
hub's sides. The connecting springs fan apart. One of the icosahedron's golden rectangles,
perpendicular to the vertical one, provides these two additional side edges.
The top icosahedron repeats this pattern. Its keel or bottom edge goes to the same two
neighbors, mirroring the springs below. Its sides reach down to grip the other two at the
mezzanine level. In a meeting-of-six, the top and bottom icosahedra involve the four neighbors
in two rectangular circuits at 90 degrees to one another. The four neighbors define a third
rectangular circuit, perpendicular to these other two.
This arrangement corresponds with the fact that the six vertices of an octahedron become
twelve as it opens up in a Jitterbug Transformation, on its way to becoming an icosahedron,
then a cuboctahedron.
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