Origami Heaven

Origami Heaven is the website of paperfolding designer and author David Mitchell

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 A Flexagon Bibliography

Suggestions for additions to this bibliography are always welcome.

Martin Gardner - Hexaflexagons - chapter found in 'Mathematical Puzzles and Diversions' - Penguin books - also published in the USA as The Scientific American book of Mathematical Puzzles and Dversions - contains the story of the discovery of the hexaflexagon by Arthur Stone and details of how to make more complex hexaflexagons. It contains the fascinating sentence 'A complete mathematical theory of flexigation was worked out in 1940 by Tukey and Feynman'.

Martin Gardner - Tetraflexagons - chapter found in 'More Mathematical Puzzles and Diversions' - Penguin books - also published in the USA as The Second Scientific American book of Mathematical Puzzles and Dversions - contains details of how to construct the Tri-tetraflexagon and various slightly more complex forms. This chapter also contains details of the Flexatube puzzle (variously also Flexotube or Flexitube) and gives the Central Line solution.

Peter Hilton and Jean Pederson - Constructing Flexagons - chapter in the author's book Build Your own Polyhedra - Menlo Park: CA Addison-Wesley - 1994 - describes how to build and flex (in a very basic way) two silverflexagons which are described here as the 4-8=flexagon and the 8-8-flexagon.

Paul Jackson - Flexagons - British Origami Society - 38 pages - is a miscellany of material relating to flexagons and other flexagon-like forms such as rotating rings and hinged cubes etc. It contains a version of Arthur Stone's theory of hexaflexagons (probably indirectly based on the work of Sidney H Scott published by J S Madachy (see below) although no acknowledgement of this is given). The booklet also includes details of Robert E Neale's remarkable Cross Flexagon.

J S Madachy - Flexagons - chapter found in 'Mathematics on Vacation' - Scribners / Nelson 1968 - contains a simplification of Arthur Stone's theory of hexaflexagons developed by the British puzzlist Sidney H Scott.

T B McLean - V-Flexing the Hexahexaflexagon - article in American Mathematical Monthly 86, 457-466 - 1979 - describes how to use the V-flex technique to find new faces of the hexahexaflexagon and analyses the possibilities mathematically.

David Mitchell - Flexagons and Flexigation - Water Trade publications - 2002 but now available online on the Flexagons page of this site - is intended to provide a simple but sound introduction to flexagons and flexigation by looking at how to construct, flex, explore, map and vary the simplest of all flexagons, the Tri-Tetraflexagon (though it also provides detailed information about methods of mapping flexagons that can be applied to much more complex examples). This booklet sets out to entertain as well as inform and several puzzles and magical effects based on the tri-tetraflexagon and its variations are explained.

David Mitchell -The Magic of Flexagons - Tarquin Publications - ISBN 1-899618-28-7 - is a full-colour cut-out and glue-together book primarily aimed at older children and younger adults. The bulk of the book consists of vividly decorated templates for eleven different flexagons, which are structured to present a series of increasingly difficult manipulative challenges. This book also contains a template for the Flexatube puzzle and gives the Easy Street solution.

David Mitchell - Silverflexagons and the Flexatube - ISBN 9780953477487 - Water Trade publications - 2016 combines into one volume David Mitchell's previous series of leaflets on silverflexagons (published in 2002), material about the Flexatube puzzle and its many solutions previously published in the first edition Lesof his Paperfolding Puzzles in 1998 and additional material on compound Flexatubes. It contains detailed explanations and maps on how to access all the known states of the Zigzag Silverflexagon, the Woven Flexitube, the First Slit-Square Silverflexagon and it's non-twisted variants, and the Labyrinth Silverflexagon.

Robert E Neale - Self-Designing Tetraflexagons - article found in 'The Mathemagician and Pied Puzzler - a collection in tribute to Martin Gardner' - Edited by Elwyn Berkelkamp and Tom Rodgers - A R Peters - ISBN 1-56881-075-X - considers various ways in which non-twisted flexagons can be constructed from a square divided into a grid of sixteen smaller squares by cutting slits or holes in the centre and/or by removing squares from the corners etc.

C O Oakley and R J Wisner - Flexagons - article in American Mathematical Monthly 64, 143-154 - 1957 - is a mathematical discussion of and analysis of hexaflexagons.

Les Pook - Flexagons Inside Out - Cambridge University Press - 2003 - 169 pages - contains a detailed analysis aand nets for many of the hexaflexagon and tetraflexagon (somewhat mosleadingly called square flexagons here) families and an introduction to several other less well known types of flexagon such as convex polygon flexagons and star flexagons. This is quite a technical book and some understanding of flexagon mathematics is required to follow all its arguments.

Les Pook - Serious Fun with Flexagons - A Compendium and Guide - Springer - 2009 - 978-9048125029 - is an unfortunately very expensive, but excellent, follow up to, and in many ways updating of, the author's previous book, Flexagons Inside Out. It concentrates on edge ring flexagons made from polygons of various shapes frrom a solid mechanics linkage perspective and shows how silver flexagons and bronze flexagons relate to these designs.