What is a trihexaflexagon?
Trihexaflexagons are part of the flexagon family. Eighteen equilateral triangles are folded into a hexagon which reveals three different faces as it is ‘flexed’.
How hexaflexagons came to be
What would you do if you discovered your school note paper did not fit into your folder?
This is the problem Arthur Stone faced when he moved from England to America in 1939, due to the different paper sizes. Arthur Stone cut his school note paper to fit into his folder and was left with long strips of excess paper.
Arthur Stone started folding the paper in different ways. He ended up folding the paper into triangles then he twisted them to form a hexagon. Once he had formed a hexagon, he continued playing with the paper by twisting and flexing it. He then noticed a small hole in the middle of the shape. As he played a bit more with the shape he was able to open it to form a new face (side) to discover the hexaflexagon!
Arthur Stone could not wait to share this discovery with his friends and together, they started a committee to investigate the hexaflexagon further. The committee wanted to understand how the hexaflexagon worked and whether it could be replicated with other shapes. After playing around and folding it in various ways, they found they could recreate it with other shapes.
The trihexaflexagon activity
This activity is designed for students to gain an appreciation of the many wonderful properties of shapes and symmetry. All the instructions and templates are provided on this page.
Students can enjoy the trihexaflexagon templates provided or you may like to download blank templates so students can experiment with their own design and try and work out what is happening to the triangles. They can also explore what happens if they fold the flexagon in a different direction and then how to get the faces to return to their correct placement. As an extension students may like to investigate how to find all six faces of a hexahexaflexagon – there are lots of templates for these available on the internet.
We love trihexaflexagons
Our Numeracy Ambassador, Simon Pampena has created some wonderful templates that demonstrate how the symmetry changes when you flex the trihexaflexagon as he explains below:
The symmetry within the trihexaflexagon, with Simon Pampena
How to make a trihexaflexagon
If you have not made one before we recommend you watch Simon Pampena make one:
How to make a trihexaflexagon, with Simon Pampena
Simon has also developed step by step instructions:
There is also an activity guide and detailed illustrations of how the triangles rotate:
2015 National Literacy and Numeracy Week design
Lower primary school students may prefer to create their own tessellation pattern or create different pictures using the Changing Shape activity.
Did you know that mathematicians have made a tessellation discovery? You can read all about it on the Helix @ CSIRO website
Double Helix also has a tessellation explorer activity you can access.