Here is a quote from the first paper cited below: Steinhaus posed a version of your question, which has become known as [*simple polygonization*](http://erikdemaine.org/polygonization/) of a set of points:
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[![Steinhaus][1]][1]
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><sup>1</sup>Agarwal, Pankaj K., Ferran Hurtado, Godfried T. Toussaint, and Joan Trias. "On polyhedra induced by point sets in space." *Discrete Applied Mathematics* 156, no. 1 (2008): 42-54.

> <sup>25</sup>Hugo Steinhaus. *One Hundred Problems in Elementary Mathematics*. Dover Publications, Inc., New York, 194.


  [1]: https://i.sstatic.net/7bQoz.png