Steiner tree four points example I have been looking at the wikipedia page for steiner trees, and I don't quite understand their 4-point solution. If the four  vertices are arranged in a rectangle shape wouldn't there be only one steiner vertex required in the middle to create the shortest length graph? The solution shows two vertices S1 and S2, but it seems that it would be shorter if there was only one vertex S instead, in between S1 and S2 and all of the vertices A, B, C, and D connect to S.
You are asking the question for Euclidean Steiner Trees. For Euclidean Steiner Tree problem one can show that "points added to the graph (Steiner points) must have a degree of three, and the three edges incident to such a point must form three 120 degree angles". That's why you need two steiner vertices instead of just one for 4 point solution. If you take just one extra point the degree will be 4 and angles also will not remain 120 degree.

To prove the property of Euclidean Steiner Trees take help of your favorite search engine. A good reference. See section 3.