A centroid hexagon is the hexagon obtained from an arbitrary hexagon by connecting, in order, the centroids of the six triangles formed by three consecutive vertices. Its opposite sides are equal and parallel (Wells 1991). A proof of the centroid hexagon result, as well as a generalization to octagons, decagons, and so on, is given by de Villiers (2007).
Centroid Hexagon
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References
Cadwell, J. H. Topics in Recreational Mathematics. Cambridge, England: Cambridge University Press, 1966.de Villiers, M. "A Hexagon Result and Its Generalization via Proof." Mont. Math. Enth. 4, 188-192, 2007.Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. London, England: Penguin, pp. 53-54, 1991.Referenced on Wolfram|Alpha
Centroid HexagonCite this as:
Weisstein, Eric W. "Centroid Hexagon." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CentroidHexagon.html