Download Serious fun with flexagons: a compendium and guide by L.P. Pook PDF

By L.P. Pook

A flexagon is a movement constitution that has the looks of a hoop of hinged polygons. it may be flexed to show diverse pairs of faces, often in cyclic order. Flexagons may be favored as toys or puzzles, as a leisure arithmetic subject, and because the topic of significant mathematical learn. conceivable paper types of flexagons are effortless to make and unique to govern. the maths of flexagons is complicated, and the way a flexagon works isn't really instantly noticeable on exam of a paper version. fresh geometric research, integrated within the publication, has enhanced theoretical realizing of flexagons, specifically relationships among differing types.

This profusely illustrated ebook is prepared in a logical order applicable for a textbook at the geometry of flexagons. it really is written in order that it may be loved at either the leisure arithmetic point, and on the severe arithmetic point. the one prerequisite is a few wisdom of undemanding geometry, together with houses of polygons. A function of the booklet is a compendium of over a hundred nets for making paper versions of a few of the extra fascinating flexagons, selected to counterpoint the textual content. those are adequately drawn and reproduced at part complete dimension. some of the nets haven't formerly been released. directions for assembling and manipulating the flexagons are included.

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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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