A 4-chromatic graph with a special plane drawing

A graph is found which is 4-chromatic, has girth 5, and can be obtained by taking a setSof points in the plane and joining two of the points whenever their distance is 1. The points inSare not found explicitly, but their existence is demonstrated by use of a computer.Subject classification (Amer. Math. Soc. (MOS) 1970): 05 C 15, 05 C 10.