DISTANCES lHnHn+1[A0] CALCULATED FROM 3-SPHERE DIHEDRAL ANGLES θHnHn+1[deg]

Dihedral angles θHnHn+1[deg] calculated from NMR data with 3-Sphere approach, a method under Hopf fibration and Lie group theories, are angles in close relationship with vicinal angles ϕ[deg], angles result from vicinal coupling constant 3 JHnHn+1[Hz]. The signs of dihedral angles calculated with algebraic equations are demonstrated with A2 root system Lie group. In attempt to find the best model for visualization of the phase angle of the pseudorotation P[deg] the proton-proton distances lHH[A0 ] between two atoms of carbon consecutives are calculated from 3-Sphere dihedral angles θHnHn+1[deg]. The string resulting from four protons around five membered rings inscribed on rectangles geometry is expected to give information about conformational constrain. Two protons on two atoms of carbon and their images on mirror are in case of cis stereochemistry inscribed on rectangle geometry using dihedral θHnHn+1[deg] and vicinal angles ϕ[deg]. In case of trans-aa and trans-ee stereochemistry are inscribed on rhombus geometry using dihedral angle with trans-aa stereochemistry and corresponding cis angle or both dihedral angles with trans-ee stereochemistry.