The strip of polygons from which a flexagon is assembled embeds neatly into the plane for triangles through hexagons, although entire polygons will occasionally overlap when the rules of connection demand it. But the first and third of three consecutive heptagons will overlap slightly when successors joined by adjacent edges, which is the rule for normal flexagons.
If a strip is prepared in advance with the intention of folding it later on to get the flexagon, the overlapping heptagons can be trimmed slightly without spoiling the effect. Nevertheless in progressing onwards to octagons, nonagons, and so on, the overlap becomes increasingly severe, and it will probably be a good idea to prepare the polygons separately, or in sparser strips, joining them in later stages of the assembly.
Once folding the strip of polygons begins, the higher order polygons increasingly resemble circles, the hinges between adjacent polygons gradually rotating around the circumference. The result is a four bladed rosette formed from two sectors and four pats, in which the transferrence of subpats from one pat to another procedes with exceptional ease and clarity. However in compensation the flexagon operation of ``rotation'' requires increasingly more versatile gymnastics. More and more tubulations also become possible as the series progresses.