Here is a quote from the first paper cited below: Steinhaus posed a version of your question, which has become known as simple polygonization of a set of points:
[![Steinhaus][1]][1]
1Agarwal, 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.
25Hugo Steinhaus. One Hundred Problems in Elementary Mathematics. Dover Publications, Inc., New York, 194.