The circles of sphere or cyclide inversion gives two isomers with trans-aa5,1 stereochemistry between 3JHH of 6 – 6.3 and 7.1 – 7.9[Hz], or one trans-aa and other trans-ee between 6.4 and 7[Hz], two dihedral angles with negative sign calculated with 3-sphere approach. The protocol for prediction all isomers with positive and negative dihedral angles predicted from vicinal coupling constant 3JHH, and calculated with the manifold equations, conic section and Villarceau circles, will be disclosed based on Hopf coordinates and Póincare theory.

Two isomers with trans-aa5,2 stereochemistry was calculated with 3-sphere trigonometric equations approach at circle inversion motion from NMR data

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