Sequence of polygons 
Hexagons
If we consider now six-sided polygons (hexagons), we see that the new hexagons do not necessarily look the same as the initial hexagon. Do they have any particular characteristics?
Indeed, only those hexagons that have the following characteristic can be obtained from an hexagon by bisection: the triangles that are defined by alternating vertices of the hexagon must share the same barycentre. The following picture exemplifies this:
The triangles \([ACE]\) and \([BDF]\) have the same barycenter \(G\)
Note also that the hexagons in the sequence of constructed hexagons seem to appear alternately with the same shape, albeit in smaller and smaller size. Furthermore, they seem to tend to an increasingly regular shape, where opposing sides are parallel to each other and parallel to one of the diagonals joining opposite vertices.
