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# Hexagram Navigator

## Canonical Taiji Contrast Cluster 2

All the permutations of opposite operations give different results. This gives enough degrees of variation amongst the hexagrams to represent all four possible states of the Taiji diagram, including change in direction of rotation.

 A: A = e(~B) A = ~C A = e(D) A = o(E) B: B = e(~A) B = ~D B = e(C) B = o(F) C: C = e(~D) C = ~A C = e(B) C = o(G) D: D = e(~C) D = ~B D = e(A) D = o(H) E: E = e(~F) E = ~G E = e(H) E = o(A) F: F = e(~E) F = ~H F = e(G) F = o(B) G: G = e(~H) G = ~E G = e(F) G = o(C) H: H = e(~G) H = ~F H = e(E) H = o(D)

The equations in the column to the left of the Taiji diagrams describe the yin/yang and positional relationships internal to each diagram. This is the Taiji Dengshi 太極等式 (the Taiji Equation). The first two columns to the right of the diagrams describe the relationships between segments in different diagrams which rotate in the same direction. The Taiji Equation and these relationships have already been described in detail in the cluster on .

The equations in the four columns to the far right of the table describe the positional relationships between segments in Taiji diagrams that have different directions of rotation. These exhaust all of the remaining possibilities for these hexagrams.

Now, the overturning of the first diagram is the third diagram, and the overturning of the second diagram is the fourth diagram. The relationships between the corresponding yang segments for the first and third diagrams is captured by the fourth column of equations: A = o(E), and between the yin segments of those diagrams by the equation B = o(F). A and B are the segments of the first diagram and E and F are segments of the third diagram.

The remaining three columns show the final permutations of opposite operators. Again, the colour coding in the cells should help identify the relationships.

 © Dr Andreas Schöter 2003-2017 Connect...