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By Bloch S.J., et al. (eds.)

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7) cannot be traversed without disconnecting a hinge, refolding the flexagon, and reconnecting the hinge. It is included because of its relationship to the trihexaflexagon. 14. It is a ring even edge flexagon (previous section). 1a). 7) by using the threefold pinch flex, in which threefold rotational symmetry is maintained during flexing.

23 point hinges are indicated by dots, and some squares are slightly separated for clarity. 23c. 1b). 23d, which has twofold rotational symmetry. In general, vertex rings can be rotated continuously, although rotation is sometimes restricted by interference between polygons. 23 Even vertex rings of four squares. (a) Box. (b) Flat, hinges diagonally opposite. 23a and b appear alternately. In this sense vertex rings are analogous to rotating rings consisting of polyhedra hinged at common edges, sometimes called kaleidocycles, as described by Conrad and Hartline (1962); Cundy and Rollett (1981); Engel (1969); Hilton and Pedersen (1994); Schattschneider and Walker (1983).

There is one possible flat compound edge ring of squares and one of regular pentagons. There are four possible flat compound edge rings of regular hexagons, two of these are included in the table. 5 Flat compound edge rings of regular polygons Polygon type Number in ring Ring symbol Square Pentagon Hexagon Hexagon Octagon Octagon Enneagon Decagon Decagon Decagon Decagon Dodecagon Dodecagon Dodecagon Dodecagon Dodecagon Dodecagon Overlapping ring. 2 Edge Rings of Regular Polygons 25 polygons. The maximum possible number of polygons in a flat compound edge ring appears to be twice the number of edges on constituent regular polygon.

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