Irregular Polygon Edge Flexagons

Abstract

AbstractMost of the edge flexagons described in Chapters 4 and 6–9 are regular polygon edge flexagons that are made from regular convex polygons. An irregular polygon edge flexagon is an edge flexagon made from irregular convex polygons. Only a limited range of irregular polygons leads to irregular polygon edge flexagons whose paper models are reasonably easy to handle (Section 2.3.1). Irregular polygon edge flexagons include some of the more interesting flexagons. Irregular polygon even edge flexagons with at least some flat main positions were briefly described by Conrad and Hartline (1962) and in more detail by Pook (2003), who called them distorted polygon flexagons. The chapter has been deferred to this point because material in earlier chapters is needed for the discussion of irregular polygon edge flexagons. Similarly, the point flexagons described in Chapters 5, 7 and 8 are regular polygon point flexagons, and an irregular polygon point flexagon is a point flexagon made from irregular convex polygons. The dynamic properties of irregular polygon point flexagons do not differ significantly from their precursors so they are not discussed.Any irregular polygon edge flexagon can be derived by replacing the regular convex polygons in a precursor regular polygon edge flexagon by appropriate irregular convex polygons. The characteristic flex for an irregular polygon edge flexagon is the same as that for the precursor flexagon. Most of the irregular polygon edge flexagons described in this chapter have at least some main positions which are, in appearance, flat regular even edge rings. Some have main positions that are irregular even edge rings. All are solitary flexagons because their precursors are solitary flexagons. In an ideal flexagon (Section 1.2), all the leaves in a flexagon are identical polygons that overlap exactly in main positions. However, there are some irregular polygon even edge flexagons that are partial overlap flexagons in which the leaves do not always overlap exactly in main positions.KeywordsEquilateral TriangleConvex PolygonIsosceles TriangleVertex AngleMain PositionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.