The hexagon obtained from an arbitrary hexagon by connecting the centroids of each consecutive three sides. This hexagon has equal and parallel sides (Wells 1991).

Cadwell, J. H. Topics in Recreational Mathematics. Cambridge, England: Cambridge University Press, 1966.

Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. London: Penguin, pp. 53-54, 1991.

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Weisstein, Eric W. "Centroid Hexagon." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/CentroidHexagon.html