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Centroid Hexagon

In a hexagon ABCDEF, connect the centroids of ABC, BCD, CDE, DEF, EFA, FAB. The result is another hexagon with opposite sides parallel and of equal length.

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"Centroid Hexagon" from the Wolfram Demonstrations Project
 http://demonstrations.wolfram.com/CentroidHexagon/
Contributed by: Jay Warendorff
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