Flexagons can become fairly complicated. The ones based on triangles are most conveniently made from long strips of paper; a roll of adding machine or calculator tape is ideal for this purpose given its convenient width. Crooked strips can be gotten by gluing faces together, or just cutting out segments and then joining them together. Leaving one extra triangle in each segment for overlapping and later gluing leads to efficient constructions.
Coloring the triangles is another problem, which can be done with crayons or markers once it is known which colors ought to be used. Aside from copying an already existent design, this is best done by drawing the Tukey triangles and then lettering or numbering the triangles in the strip. That information is sufficient to fold up the strip, since pairs of consecutive numbers are to be hidden by folding them together. Painting can be done before folding by following a color code for the numbers, or after the folding is done, when the faces can be painted wholesale, or even embellished with designs.
Other flexagons, even the ones folded from ``straight'' strips, require a higher degree of preparation, although it is relatively easy to assemble a collection of primitive components which later can be glued together according to the necessities of the individual flexagon.
Figure 1 shows seveal candidates for tetragonal flexagons. The square, being a regular 4-gon, wiull lead to mormal flexagons which will lie flat with only two sectors.. However, the rhombus, with and angles will lie flat with three sectors, and still produce a very attractive flexagon. Trapezoids also give good flexagons, especially when made with a choice of these same angles.
All of them are susceptible to recursive elaboration, although the presence of different angles will lead to somewhat different shapes while they are being flexed if the recursion is not applied uniformly throughout.