Transforming a 3D into a 2D Plot

I have a ListPointPlot3D in which all points lie on a plane. I’d like to transform it into a simple 2D Plot by looking at the points from an orthogonal direction to that plane, but I don’t know how to do it. (The following is a MWE, not my actual data).

 points = Flatten[Permutations /@ IntegerPartitions[1, {3}, Range[0, 1, 1/5]], 1];  ListPointPlot3D[points]