Hooke’s Joint Flexagons

Updated 28 January 2010.

Hooke’s joint flexagons were first described by Engel, who calls them ‘hybrid flexagons’, but ‘Hooke’s joint flexagons’ is more apposite. I use this term in my book ‘Serious fun with flexagons’, and describe one on pp. 321-323. This flexagon is also described at Hooke Click the link.  Two more are described, under different names, on pp. 88-89 of my book ‘Flexagons inside out’. For a Hooke’s joint flexagon called the never ending card see the following
http://www.victorineoriginals.com/images/samples/instructions/neverendingcard.html 
http://www.mathematische-basteleien.de/magiccard.htm

The characteristic feature of a Hooke’s joint flexagon is that adjacent leaves are hinged to either face of an ‘intermediate leaf’’ The hinges are at right angles so the intermediate leaf is a Hooke’s joint. The never ending card is a shape changing flexagon because the hinges are not symmetrically placed on an intermediate leaf.

The simplest Hooke’s joint flexagons have four leaves connected by four Hooke’s joints. A wide range of forms is possible, as illustrated by the four mentioned above, all of which have four leaves.

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