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added 25 characters in body
Joseph O'Rourke
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As this construction was new to me, I wanted to see it. Here are two random examples. The green points are centroids of the triples of points.


http://cs.smith.edu/~orourke/MathOverflow/FivePointsr34.jpg
Joseph O'Rourke
  • 150.9k
  • 36
  • 358
  • 958