Steiner minimal trees on regular polygons with centre Original Research Article

Let Pn, n ⩾ 3, be the set of vertices of a regular n-gon and o be the centre of Pn. Let Pn+ = Pn +∪{o}. In this paper we determine the Steiner minimal trees on Pn+. By this example we will see how complicated the Steiner problem may become if even one regular point not lying on the Steiner polygon is added.