Computational Thinking: HexaHexaFlexagon Automata is a full colour booklet on computational thinking based around exploring strange mathematical paper models called flexagons. Make the flexagon and explore it while at the same time learning about computing and computational thinking and how it can help. The free booklet is written by Paul Curzon of Queen Mary University of London based on the CS4FN approach.
Above: Vi Hart explains what a hexaflexagon is and their history.
Above: How to fold a hexahexaflexagon, with Paul Curzon.
Hexaflexagons have three faces (with one hidden), hexahexaflexagons have more hidden faces.
- Download the full colour booklet: Computational Thinking: HexaHexaFlexagon Automata (full colour)
- An earlier black and white plain text version is also available: Computational Thinking: HexaFlexagonAutomata (plain text).
- Download a template to make a basic hexahexaflexagon. Ideally enlarge to A3 to print.
- Download a page containing 4 hexahexaflexagon templates for easy printing of class sets. Ideally enlarge to A3 to print.
- Download the linked classroom activity sheet: The HexaHexaFlexagon Automata (forthcoming)
- Linked slides [PPT]
- See ‘More downloads‘ at the end for activities for younger kids
- Make a red and yellow hexahexaflexagon by folding and gluing a multicoloured paper strip, following the algorithm. Once made you start to explore it. As you fold it up and unfold it, you magically reveal new sides as the flexagon changes colour. To explore it fully, you need a map. A graph seems a good representation, which you create as you explore.
- A graph is like a tube map, with circles (nodes) for places revealed and lines between them (edges) showing which circles you can move between by folding and unfolding the flexagon. It is a special kind of graph that can be thought of as a machine – a ‘finite state machine’. The nodes of the graph are different states the flexagon can be in and the edges show what actions that can be taken to move between states. It describes the computations involved in flexing the flexagon. A finite state machines is a very useful tools in the computational thinking toolbox. They are an important way for describing what computer systems do.
- Learn about graphs, graph exploration algorithms, finite state machines (also called automata), specification, computational thinking, abstraction, data representation, computational modelling, generalisation and pattern matching, algorithmic thinking, evaluation, logical thinking.
- Turn it into an Art activity: Draw different images on the different sides to create art where the images appear and disappear all on a piece of paper. Some sides will appear scrambled. Perhaps you can create drawings so when scrambled the sides just turn into a different image.
- Create hexaflexagon christmas cards. Create a graph-based map of your christmas card to allow you to keep track of what is where. Give it to the recipient in a sealed envelope as the ‘solution’ to the puzzle showing how to find all the messages.
Easter hexaflexagon – this is a three-faced flexagon (two visible faces and one hidden (‘find the rabbit’)) with an Easter theme. Black and white for colouring in.
Christmas hexahexaflexagon – this is a six-faced flexagon (four hidden faces) with a Christmas theme. Both black and white for colouring in (and ready-coloured to save time).
More of our resources, including linked classroom activities can be found in our resources section.