TETRAHEDRAL  STRUCTURES  &  SYSTEMS
The word "tetrahedral" is an adjective, created by splicing a new ending onto the noun form, which is "tetrahedron".

In geometry, a tetrahedron is formed by assembling four different triangles into a 3-dimensional structure, where:
(1) one triangle forms the base, and
(2) the other 3 triangles (each one attached to the base, along one edge) slope upward, lean against each other, and create/share a single peak.

They are shaped similar to an Egyptian pyramid, except pyramids have square bases, while a "tetrahedron" has (necessarily) a triangular base.
 
Here are two example drawings of tetrahedrons:
tetrahedron-colored.jpg
tetrahedron-pipes.jpg

Tetrahedrons become remarkable things, once you understand their patterns and principles. Because they are made from the absolute smallest possible number of triangles -- which, as described in the prior pages, are the strongest TWO-dimensional shapes that can possibly exist in the universe as we know it -- tetrahedrons are the strongest and most stable THREE-dimensional shapes that can possibly exist, in the universe as we know it. Stated in other words, if you were to set out to create the absolute strongest possible frame that you could design, to hold and contain something of great value to you, then you would be well-advised to seriously and carefully consider how you might use some sort of tetrahedral frame, to accomplish that goal.

 

Since "tetrahedral" is an adjective that can be adapted to refer to a very wide variety of nouns, the word itself needs to be considered, and understood, in the context of some of the wide array of variants it can be adapted and applied to. The crucial test is whether the number "4" is truly a central and crucial element, in how some type of structure or system is built, and arranged.

 

For example, all vertebrate animals that live on land (except snakes) can be called tetrahedral organisms, since they all have exactly four main limbs. In most animals, the main limbs are grouped into forelegs, and hindlegs; in bats and birds, they are grouped into wings, and feet; and, in chimps and apes, they are grouped into arms/hands, and legs/feet. All higher animals use that system, for a combination of two different clusters of reasons:

(1) When the first weird-shaped fish began to develop and use the abilityh to cross short stretches of land, either to flee from a predator in the water, or to reach some other body of water, the fish that could move most quickly and efficiently, across land, were those fish which had two large fins near the front of their bodies, and two large fins near the posterior. Those formed the starting point, for the evolution of other, better-adapted types of limbs. 

(2) There are also issues of logic, and functionality; the number 4 happens to sit at the sweet spot, where it can balance each and all of the following needs/uses:

(A) the need for slow but stable mobility . . . since one leg can be raised, to look and/or feel around for the next landing spot, while the other three legs will continue to provide a stable tripod, to support the animal as it walks, stalks, evades, etc.;

(B) the need for speed . . . as shown by the way horses, dogs, cheetahs, and other fast-running animals developed synchronized galloping movements, which coordinated the two forelegs into a single coupled pair, and the two hindlegs into a different but single coupled pair; and,

(C) the need to limit the amount of brain capacity, which must be allocated and dedicated to handling the numbers of neuro-muscular signals that must travel both to, and from, the smallest number of limbs which can provide the functions that animals must have to survive and reproduce.

In similar ways, cars and trucks are tetrahedral machines. Why? Because they use exactly four wheel/tire units, for both support and travel, and those four units are carefully positioned around the periphery of any car or truck, at or near each of the four corners of a generally rectangular unit. People have tried to design and build cars with only three wheels, but those have nowhere near enough stability to enable the speeds, and the safety, of four-wheeled cars and trucks.


Many other types of tetrahedral systems and structures can be named; and, it sould even be pointed out, here and now (and as described in more detail in the "Sigma/Delta" pages of this website) that even a simple pair, made of only two people, will also work best, if both of those two people also recognize and respect that, in a healthy and well-balanced relationship, they are actually creating the two other, additional components of their larger functional unit.

 

In addition to the two individuals, who will indeed remain as different and distinct indivudals, the THIRD component of what hey have created can be called "the sigma component", named after the Greek letter (i.e., sigma) that is used in math equations to represent a sum, which was created by adding two or more things together. The "sigma" part of a partnership is the "entity" which two people create, if and when they act together. That entity can be given a dozen different names, such as the couple, the pair, the team, the partners, the family, the company, or any of a dozen other words, in other types of situations.

And, the FOURTH crucial component, of that relationship between two people, is called "the delta component", named after the Greek letter ∆ (delta), which is used in math equations to represent the difference between two quantities (such as, the change in velocity that some object undergoes, as a function of time, location, acceleration, etc.). As described in more detail, on other pages, if two people on a team (or in a family) can learn to not just tolerate, and grudgingly accept, the differences between them, and can learn, instead, to welcome, respect, appreciate, fertilize, cultivate, and encourage those differences, as sources of balance, diversity, interest, amusement, productivity, and teamwork, then they will have a better, happier, more stable, more rewarding relationship.


This is not meant to say that tetrahedrons, or the number 4, have some sort of magical or mystical powers. Instead, it is a statement, and a recognition, that the number "4" is where -- in many instances, and many settings -- components can and will begin to work, function, and cooperate together, in ways that convert them from (i) mere collections of components, into (ii) functioning systems and structures, which rise up to higher levels of capability, and functionality, than the components, alone, could achieve.