Flexagons (original) (raw)
Flexagons are fascinating, origami-like puzzles folded from strips of paper that you flex in various ways to reveal previously hidden portions of the flexagon.
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The book The Secret World of Flexagons: Fascinating Folded Paper Puzzles is now available at your favorite bookstore or directly from the publisher.From the introduction: "Flexagons sit at the intersection of paper folding, puzzles, and mathematics. You could choose to enjoy the pleasure of using your hands to flip through a kaleidoscope of arrangements. Or come up with interesting ways to decorate them. Or explore what's hiding inside, possibly discovering new flexes and new types of flexagons. Or challenge yourself to figure out how to "solve" a flexagon in the same way you might solve a Rubik's Cube. Or investigate the mathematics that can untangle how the twisted strips of paper actually work. In this book, we touch on each of those areas, leaving it up to you which of these most interest you." | |
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Explorable Flexagons is an interactive, online book that teaches you about a variety of flexagons and flexes. |
Flexagons are simple to create from a piece of paper by cutting, folding and pasting. Most people start with the pinch flex on a triangle hexaflexagon or square tetraflexagon. From this page, you can get to templates for a wide variety of flexagons of different shapes, new types of flexes, interesting puzzles and some theory.
For an interactive introduction to a variety of flexagons and flexes, see Explorable Flexagons.
For information on flexagon talks at the Gathering For Gardner, see G4G13 or G4G10.
Triangle Flexagon Bestiary
- Tetraflexagons
- Pentaflexagons
- Hexaflexagons
- Heptaflexagons
- Octaflexagons
- Enneaflexagons
- Decaflexagons
- Dodecaflexagons
- Templates for "braids"
Quadrilateral flexagons
Point flexagons
- Interleaf foldings of edge flexagons predicted by the characteristics of the corresponding point flexagon
Flexes
- Flip flex
- Pinch flex
- Pivot flex
- Pocket flex
- Pyramid shuffle flex
- Silver tetra flex
- Slot flex plus more details
- Slot-tuck flex
- Ticket flex
- Tuck flex and single flap flex
- V flex
- Flex notation
- Flex generating sequences
- Cycles and traverses
Puzzles, mazes, etc.
- Silver tetraflexagon illusion
- Pyramid flexagon maze
- Bronze hexaflexagon puzzle
- Octaflexagon puzzle
- Magic square tetraflexagon and Magic octaflexagon
- Enneaflexagon maze
- Decaflexagon puzzle
- Tridodecaflexagon puzzle
State diagrams
- 5 sided hexaflexagon - state diagram of a hexaflexagon using five different types of flexes
- 11 leaf hexaflexgon
- 12 leaf hexaflexagon
- Two pentaflexagons from different generating sequences only involving the pyramid shuffle
- 15 sided hexaflexagon - several state diagrams for 15 sided hexaflexagons made from a straight strip of paper
- Slot flex diagram - shows shape-shifting states using the slot flex and pocket flex on a 5 sided hexaflexagon
- Point flexagons contains diagrams of various flexagons
Theory and terminology
- Flex Theory paper contains:
- flex notation, useful for describing sequences of flexes
- pat notation, useful for describing the internal structure of a flexagon as it changes during flexes
- Notes on flexagon naming
- Tips for creating new flexagons
- Definitions
- Multi numberings for flexagons