None of the first three varieties of convex polygon flexagon, described in the previous chapter, is typical of the family. The fourth variety, pentagon flexagons, and higher varieties have characteristics in common and all can be regarded as typical members of the family. Some are twisted bands and so exist as enantiomorphic (mirror image) pairs.

In a typical convex polygon flexagon the sum of the leaf vertex angles at the centre of a principal main position is greater than 360° so the principal main position is skew and its outline is a skew polygon. For a typical convex polygon flexagon with a single complete principal cycle the number of main positions in the principal cycle is the same as the number of sides on the constituent polygons. It is always possible to traverse the principal cycle without bending the leaves of paper models. There is always at least one subsidiary cycle. In general subsidiary cycles cannot be traversed without bending leaves. The appearance of the subsidiary main positions is different from that of the principal main positions. The number of main positions in a subsidiary cycle is either the same as the number in the principal cycle, or a factor of this number. Where the numbers of main positions in subsidiary cycles differ, so do the appearances of associated subsidiary main positions. When bending of leaves is allowed it is possible to traverse from a given intermediate position to any other intermediate position via just one main position.

In a principal main position a typical convex polygon flexagon has two possible configurations. […]