The Ternary Classification

The classifications based on the stack of 12 for various fields I have attempted until now have the dominant symmetry 3*4. The outer aspect is ternary and the inner is quaternary or rather dual binary. For example for Mathematics;

(((Number,Function),(Operation,Equation)),
((Set/Logic,Analysis),(Algebra,Geometry)),
((Probability,Statistics),(Computation,Information)))

and for Physics;

((((Energy,Time),(Momentum,Distance)),((Angular-Momentum,Area),(Spin,Volume))),

(((Mass,Gravity),(Electric-Charge,Electric-Field)),((Weak-Charge,Weak-Field),(Strong-Charge,Strong-Field))),

(((Higgs,Atom),(Boson,Planet)),((Lepton,Star),(Quark,Black-Hole))))

 

The one for Physics has the symmetry of 3*4*2=24, and its outer shape is still 3.

 

If 3 words are assigned for the elements of this ternary symmetry they would probably be;

 

(Measure, Theory, Application) 

Previously I have mentioned the number triplet (0,1,∞) which also has ternary symmetry and this suggests Zero and Infinity have Binary symmetry. They are inversions of each other around unity anyway.

Why 3 dominates over 2 is open for investigation.