12 Degrees of Freedom
"By tetrahedron, we mean the minimum thinkable set that would subdivide Universe and have interconnectedness where it comes back upon itself. The four points have six interrelatednesses. There are two kinds of number systems involved: four being prime number two and six being prime number three. So there are two very important kinds of oscillating quantities numberwise, and they begin to generate all kinds of fundamentally useful mathematics. The basic structural unit of physical Universe quantation, tetrahedron has the fundamental prime number oneness."

Bucky Fuller.  Synergetics. 620.03
 

The Tetrahedron
The mathematics involved in synergetics consists of topology combined with vectorial geometry. Synergetics derives from experientially invoked mathematics. Experientially invoked mathematics shows how we may measure and coordinate omnirationally, energetically, arithmetically, geometrically, chemically, volumetrically, crystallographically, vectorially, topologically, and energy-quantum-wise in terms of the tetrahedron.
There is not one but many mathematics and for numerous reasons each fails to satisfy the members of the opposing schools.  It is now apparent that the concept of a universally accepted, infallible body of reasoning -- the majestic mathematics of 1800 and the pride of man -- is a grand illusion.

Morris Kline. Mathematics: The Loss of Certainty.
Competing mathematical systems need only demonstrate internal consistency based on a set of accepted initial assumptions.  They did not have to necessarily provide an accurate representation of the physical world.
The tetrahedral and vector equilibrium models in the isotropic vector matrix (what Bucky discovered is the coordinate system within which Nature carries out her transactions) provide an absolute accommodation network of energy articulation, including the differentiated proclivities of:

associative-disassociative

convergent-divergent-oscillating-pulsating

dynamic-kinetic

energetic-synergetic

entropic-syntropic

expansive-contractive

explosive-implosive

gravitational-radiational

hydraulic-pneumatic

importing-exporting

inside-outing-outside-inning

involuting-evoluting

omnidirectional-focal push-pulling

radial-circumferential

rotational-ovational gearing

synchronous-dissynchronous

torque-countertorque

turbining-counterturbining

vector-tensor
together with the integrated synergetic proclivities of:

inward-outward and three-way aroundness;

precessional processing of plus-minus polarization; and

wave propagation mechanics;
together with the intertransformative behavioral phases of:

incandescent

liquid

plasmic

thermal

vapor;
and the mensurabilities elucidating the disciplines of:

biological

chemical

cryogenic

crystallographic

electrical

genetic

geodesic

geodetic

geological

geometrical

logical

mathematical

mechanical

nonbiological structuring

physiological

scientific

teleologic

thermodynamic

virological
explorations for comprehensive rational interrelationship number constants.