Fundamental Compound Edge Flexagons

Abstract

Compound edge flexagons are even edge flexagons with main positions that are, in appearance, compound edge rings of regular convex polygons (Section 2.2.4). In a compound edge ring, alternate hinge angles (Fig. 1.3) are the same and, in general, alternate polygons are the same distance from the centre of the ring. Compound edge flexagons with at least some flat main positions were briefly described by Conrad and Hartline (1962) and in more detail by Pook (2003). A compound edge ring of 2n regular convex polygons, and corresponding compound edge flexagons, can be divided into n identical sectors each containing two polygons. All the possible flat non overlapping, compound edge rings, containing up to ten polygons, with up to 12 edges on the constituent polygons are listed in Table 2.5. Possible non flat compound edge rings of four regular polygons, with up to eight edges on the constituent polygons, are listed in Table 2.6.