Vertex polygons (Q1950966)

Given an \(m\)-sided polygon, a vertex \(n\)-gon is an \(n\)-sided polygon formed using \(n\) vertices of the \(m\)-sided polygon. An equal-\(n\)-gon polygon is a polygon, for which all vertex \(n\)-gons have the same non-zero area. The definitions are generalizations of vertex triangles and equal-area polygons introduced by \textit{G. Harel} and \textit{J. M. Rabin} [Am. Math. Mon. 110, No. 7, 606--619 (2003; Zbl 1046.51008)]. The author proves a result that gives necessary conditions for an equal-area hexagon to be also equal-quadrilateral. Furthermore, a method to construct equal-quadrilateral hexagons is given and extended to equal-\((n+1)\)-gon polygons.