Steiner polygons in the Steiner problem (Q1337104)

The Steiner problem for a set \(A\) of \(n\) points \(a_ 1, a_ 2, \dots\), \(a_ n\) (called regular points) in the plane is to construct a shortest network connecting these points, possibly with additional points. The shortest network is a tree, called the Steiner minimal tree on \(A\). A polygon whose vertices are points of \(A\) is called a Steiner polygon of \(A\) if all Steiner minimal trees of \(A\) lie in it. \textit{E. J. Cockayne} [SIAM J. Appl. Math. 18, 150-159 (1970; Zbl 0218.90064)] found that a Steiner polygon can be obtained by repeatedly deleting triangles from the boundary of the convex hull of \(A\). The author generalizes this concept and gives a method of constructing Steiner polygons by repeatedly deleting \(k\)-gons (\(k \leq n\)).