More about Hexaflexagons

I first met hexaflexagons in “Mathematical Puzzles and Diversions” by Martin Gardiner. First published in 1959 though my copy comes from 1975.

The shapes were discovered by British mathematician Arthur H. Stone in 1939 when playing with strips of paper he had cut off the US sized paper to fit it into his UK shaped binder. The strips end up being joined with a twist and so form what mathematicians call a Moebius Band. You may have met something similar when making an infinity scarf.

The hexaflexagons in my book were designed to be made in paper but I am showing you how I made a few different designs in crochet. You can make hexaflexagons with different numbers of sides. The simplest has three sides and may be referred to as a tri-hexaflexagon; this is the sort that I have made.

Over the years I have made them from time to time. They are quite good for containing birthday or other messages as you can only see two of the three sides at any one time.

Having decided to make a crochet hexaflexagon for a 50th birthday, which morphed into making two crochet hexaflexagons and a pattern and an ebook, I made several in paper.

paper hexaflexagons

There is a very useful place to obtain templates for making paper ones called Aunt Annie’s Crafts –

Even more information and templates can be found here –

A search will find many more.

My inspiration for the birthday one was “Find the Rainbow”

birthday hexaflexagon

because using the same colour on both sides meant it was possible to tantalisingly have the six basic rainbow colours with thee on one side and three on the other but to flex round to the view above, as I showed you before.

showing movement

Having successfully worked out how to achieve this in crochet, like with the Hexatetraflex, my mind turned to more ambitious projects.

You can see me playing with different arrangements of triangles in the top photograph.

And so the second more considered hexaflexagon was born.

diagram of movement

So of course I was by now so pleased with the whole thing that I decided to create a pattern (in both UK & US terms of course) and to create an ebook containing all three of my Flexy patterns.

cover of ebook

The font for the title is called “Ink Free” and I thought it captured the sense of fun so well.

I have decided to charge a modest £2 for the Hexy Flex pattern and £6 for the ebook.

The pattern for what I have decided to call a Hexy Flex is here –

and for the ebook here –

I find it interesting to realise that all these patterns have been inspired by my daughter and her love of such things and my desire to make her something in crochet as a present.

When I saw her recently she mentioned that a hexa-hexaflexagon would be even better, (That would be one with six different sides of course and actually fifteen different arrangements.) although she felt that this would not be possible because of the thickness involved. I am not sure that it might not be possible working in a slightly different way, though trickier to create a pleasing design. So I find myself spending an inordinate amount of time making hexa-hexaflexagons in paper to understand how they work.

paper hexa-hexaflexagons

I may of course be disappointed if I ever spend the time and effort to turn my final design into crochet, so although I am having fun, maybe I should consider making a simple ‘proof of concept’ version before I try to make something more complicated.


4 thoughts on “More about Hexaflexagons

    1. I do think that my Hexatetraflex would be particularly good for that purpose. I find it quite soothing to fiddle with myself and it is so easy to manipulate. The Flexacube and Hexy Flex require a bit more thought. Don’t know if that would be good or bad.


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