A facebook posting reminded me of something I used a lot when I was in school and had forgotten all about them. We used them for sending secret messages to each other. I am talking about hexaflexagon. Technically, a flexagon is a flat model, constructed by folding strips of paper that can be flexed or folded in certain ways to reveal faces besides the two that were originally on the back and front. Flexagons are usually square or rectangular (tetraflexagons) or hexagonal (hexaflexagons). A prefix is added to the name to indicate the number of faces that the model can display, including the two faces (back and front) that are visible before flexing. For example, a hexaflexagon with a total of six faces is called a hexahexaflexagon. There are many of these and many ways to make them, but I thought I would show you the one that I know which is a trihexaflexagon.
What you will need. A piece of paper, scissors, glue and a protractor. (Sorry the glue is missing in the picture. You can use a glue stick or I used Elmers.
I remember reading about Flexigons in SciAm while in Jr. High School. And colored the faces, concealed messages, etc. The mma.org link is interesting as Bryant Tuckerman, Richard Feynman, and John Tukey are mentioned on page 3 as some who worked with flexigons.
Or you could watch this :
This video is based on, and in honor of, Martin Gardner's first Mathematical Games column from 1956, "Hexaflexagons," which can be found here: http://maa.org/pubs/focus/Gardner_Hexaflexagons12_1956.pdf
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