Flexagon Challenge

If you want to test your flexagon skills, check out the dodecaflexagons. Below is a tetra-dodecaflexagon with fractal faces folded from a hexagonal template.

tetradodeca

Triflex with Pattern

Here is a Trihexaflexagon with an interesting color pattern.  Fold as for other Trihexaflexagons.

Triflex with pattern
The Flexagon Portal

Flexagon.net was created to provide a place for all those interested in flexagons to share their ideas, templates, or anything related to flexagons. Here is what you will find:

  1. Original flexagon templates - For some of the templates, each triangle or polygon unit is separately labeled and every corner coded.  This allows one to more easily discover all the combinations of faces and rotations of the polygons.
  2. Information on technical aspects of flexagons and on creating flexagons.

 Flexagons continue to stimulate interest from recreational mathematicians, artists, paper folders, and even from serious mathematicians.  Check out the great templates below.  Please feel free to give me comments from the contact page.  I am also a member of the Yahoo Flexagon group .

Note:  The following templates are free for personal or classroom use. Anyone that wants to use these for publications either written or Internet, must contact me for approval. (see Contact Me tab)

Trihexaflexagon
Classic

 trihexaflexagon

This is the classic 3 faced hexaflexagon.  This template is created to be easy to cut out, glue and fold up.  This fresh design has been nicely labeled to best show off the mathematical properties of the flexagon.  Everyone should make one of these!

Tetrahexaflexagon

tetrahexaflexagon

This flexagon is not nearly as widely known and folded, but it is almost as easy to cut out and fold up as the classic.  The four faces provide opportunity for design creativity. A well folded model will flex very smoothly with well formed faces.

Pentahexaflexagon

Hexahexaflexagon
Variatiion A

hexahexaflexagon

Hexahexaflexagon
Variation B

hexahexaflexagon

Hexahexaflexagon
Variatiion C

hexahexaflexagon

The Snake
Heptahexaflexagon
Variation A

heptahexaflexagon

 

Heptahexaflexagon
Variation B & C

heptahexaflexagon
 
Template for the B and C variations of the 7 faced heptahexaflexagon.  Both variations are folded from the same template.  Within each folded variation, you can see the faces of the other variation.  Be sure to check out the "G" and Sunday face on both variations.  Challenge - Can you V-flex from one variation to the other?  This is the hexaflexagon with the smallest number of faces that will fold up into two flexagons with different Tuckerman state diagrams.
 

Fire and Wood
Heptahexaflexagon
Variation D - Now available for Download!


heptahexaflexagon 4
 
Template for the D and last variation of the 7 faced heptahexaflexagons. This is the hexaflexagon with the smallest number of faces where the template curls on top of itself.  In fact the template has three spirals in it.  This flexagon is a bit more challenging than the others on this page to make due to the more complex template.  One of many interesting things about this flexagon is that if you start with the E face on top and the F face on the bottom, you can flex 5 times from the same corner.  Give it a try.
 
 

What's New?

Sangaku Flexagon

TriHexaflexagon with Sangaku Japanese Temple Geometric problems for faces.  For details on problems see 2008 book by Fukagawa Hidetoshi and Tony Rothman, Sacred Mathematics .

Tetra-Flexagon article from Russian journal: Nauka i Zhizn (Science and Life) ~1970,

All variations of 8 sided Hexaflexagons.

Method to create Hexaflexagons with any number of sides! 

3 - 6 sided Hexaflexagon maps  

Dodeca flexagon frieze patterns

Dodeca Flex!

Make a Flexagon Now!

Find out why so many people like these things, download flexagon models to print, cutout, fold and flex! 

 Flexagon with Three Faces

They come in squares too!  GIve this one a try!

tetratetraflexagon

Cyclic Square Flexagon with 4 faces 

Flexagon Poll

Vote for your Favorite Flexagon