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  1. Does this result above six points follow have a name?

Let $A$, $B$, $C$, $D$, $E$, $F$ be six points in the plane and $AB, CF, ED$ are concurrent and $BC, DA, FE$ are concurrent then $CD, EB, AF$ are concurrent.

  1. Can generalized of this result to higher dimensional spaces?

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That is the dual of Pappus Theorem i believe: https://en.wikipedia.org/wiki/Pappus%27s_hexagon_theorem.

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