### M Theory Lesson 292

In the March 09 paper, The S-matrix in Twistor Space, we find Hodges diagrams related to the BCFW recursion rules. Ignoring edge and vertex information, the butterfly identity looks like and the Poincare dual of the right hand graph gives which brings the rule down to the familiar exchange relation: On the other hand, a Poincare dual of the left hand graph does not immediately return the other graph, up to a square diagonal, but we see that the resulting graph is closely related as in the usual cyclic operad correspondence between polygons and trees.

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