A hexaflexagon is a paper hexagon that is folded from a strip of paper. As the sides are flexed, or moved, they reveal more surfaces than a standard hexagon would. My recommendation, when following the instructions, is to color the front face with the 123123123 colors, then fold and glue everything together and then color the remaining three faces after its been folded. Bruce mclean first published an article on the vflex in 1979 with a more recent article mapping the 9 sided hexaflexagon using the pinch flex and vflex below is a diagram mapping out the states of the 5 sided hexaflexagon using the. Very, very, very addictive you can use any rectangle to make this, i am just using printer paper. Doing a pinch flex on side 1 gives you a cone with 3 on the inside. This file contains additional information, probably added from the digital camera or scanner used to create or digitize it. Do not open up one side of the flexagon separately before opening up the other. People have been exploring the hexaflexagon using the pinch flex and the tuckerman traverse since the 1930s see the wikipedia article for more information.
To do some mathematical investigation you first need to learn how to flex the flexagon correctly. Complex flexagons can also incorporate parts of solitary flexagons. Find out what they have to do with computational thinking by downloading the cs4fn booklet. How to make a trihexaflexagon folding a 60 o angle 60o 1 2 3 1. Note that the word hexaflexagons with no prefixes can sometimes refer to an ordinary. Hexaflexagons are sixsided shapes made from folded paper which may be flexed or folded, and opened out to reveal hidden faces. If the file has been modified from its original state, some details may not fully reflect the. Also, the flexing action is so therapeutic that you wont want to stop. This origami hexaflexagon is an action model paper design. Information from its description page there is shown below. Your strip should now resemble that used to make the trihexaflexagon. Print blank flexagon pattern on one sheet of paper, singlesided. The figure can be flexed to show six different faces.
In this video i will how you how to make this origami flexagon with a single sheet of paper. Any of these searches should yield many patterned templates to choose from. Make a red and yellow hexahexaflexagon by folding and gluing a multicoloured paper. Youll also notice that some faces appear more often than others. As you fold it up and unfold it, you magically reveal new sides as the flexagon changes colour.
Wikipedia contains a nice printable pdf template for a hexahexaflexagon that we followed successfully. Download hexaflexagon template for free formtemplate. This may lead to panels from different faces getting mixed together. Flap 1 flap 2 3 3 3 3 3 3 0 0 0 0 0 0 1 1 1 1 1 1 7 2 7 7 7 7 2 2 2 2 2 8 8 8 8 8 8 7 5 4 4 4 4 4 5 4 5 5 5 5 6 6 6 6 6 6 a a a a a a b a c b a a b c a c c b a b c b. Push three corners down and in to make three valley folds.
Make a fold from one corner, so that the other corner lands on the first fold 3. A hexaflexagon is paper disc that looks like it has two sides, a front and back, but when you flex it, the hexaflexagon reveals six 6 different faces. The flexagons in this project have six colors faces. Download the booklet hexahexaflexagon automata download the booklet hexahexaflexagon automata make a red and yellow hexahexaflexagon by folding and gluing a multicoloured paper strip, following the algorithm. Fold so that the triangles labelled 4 face each other, as do the triangles labelled 5 and the triangles labelled 6. Videos novos todas as tercas e, quinzenalmente, aos sabados, as 11h30. Blank template with instructions also a pdf version. The four faces provide opportunity for design creativity. You are essentially wrapping the paper into a spiral. Interestingly, in a hexahexaflexagon, each of the colored faces can appear in two different orientations such that, if you were to draw a sixpointed a star at the center of your hexagon, it would sometimes appear around the center and sometimes around the outer edges. Origami tutorial geometric printable templates 45 ideas for 2019 printable pattern fortrihexaflexagon with stars papercrafts papercraft cardm.
Make the arc for the final points of the triangles. Fold over the last triangle and glue in place yielding figure 6. Free kitchen appliance user manuals, instructions, and product support information. Fold back along line ab, and then back along line cd, yielding figure 4 and then 5. Most of the more interesting flexagons for which nets have been published are complex flexagons, and.
This special kind of map is called a finite state machine. On this page you will find instructions on folding four different types of hexaflexagons. You can pre crease all tria ngles before and after gluing. Turns out its a good time to sell shirts because its black friday, and the entire store is 20% off. Yes, weve been encouraging recreational use of hexaflexagons and even hexaflexagon parties to happen on oct. Heres the state diagram for the 5 sided hexaflexagon shown above. Some sides can appear in more than one state with a different centre. For the three sided version, fold adjacent 3s together and tape the tabs onto the appropriate faces labeled with a 2. The characteristic flex for a complex flexagon is the same as that for the precursor flexagons. A flexagon is a polygon, usually made from paper, that can be folded in. Printable template making a flexagon print a template. Hexaflexagons amazing shapes investigation ib maths. If youre behind a web filter, please make sure that the domains.
Blank and decorated hexahexaflexagon template free. Find owners guides and pdf support documentation for blenders, coffee makers, juicers and more. Hexahexaflexagons are strange folded objects that have hidden sides. One hexahexaflexagon, constructed from an irregular paper strip, is almost identical to the one shown above, except that all 18 configurations can be flexed on this version. Hexahexaflexagon instructions printing a blank flexagon flexing assembly print blank flexagon pattern on one sheet of paper, singlesided. The resulting angle will be 60o flip 3 3 3 3 3 3 1 1 1 1 1 2 1 2 2 2 2 2 x x 1st fold fold 3s away 2nd fold hide the 2s the simplest hexaflexagon is the. Commons is a freely licensed media file repository. Make a line segment long enough for 19 triangles how to makeem. Instructions and patterns for making hexahexaflexagons. The magic of flexagons paper curiosities to cut out. If unable to align doublesided printing, print front and back patterns on two sheets, singlesided.
If youre seeing this message, it means were having trouble loading external resources on our website. Free download hexaflexagon template pdf, 873kb and customize with our editable templates, waivers and forms for your needs. Constructions front hexahexaflexagon supplies coloring front make the sides of the triangles. I find it can be easier especially if you use a fast drying glue to leave the inside uncut until after gluing together. The models were named hexaflexagons hexa for their hexagonal form, and. Search online for flexagon, hexaflexagon, or trihexaflexagon templates. You make a red and yellow hexahexaflexagon by folding and gluing a multicoloured paper strip in a special way. For example, here are the six faces of one of my own hexaflexagons. Hexaflexagons this page is a workinprogress collection of free templates and videos about hexaflexagons.
Hexahexaflexagon instructions printing a blank flexagon. Blank and decorated hexahexaflexagon template free download. Happy hexaflexagon month, in honor of martin gardner. Hexahexaflexagon craft project crafts, craft projects. Then fold the third triangle down from the left triangle back. To color the faces of a hexahexaflexagon completely, in other words, you will need six. This video will show you how to make your very own hexahexaflexagon. A hexahexaflexagon is a flexagon made of six sides each containing six smaller triangles. Tuck the different colored triangle underneath the other one.
Sep 27, 20 some ideas for investigations into flexagons are taken from a fantastic book on the subject by the art of mathematics available to read as a pdf here. Hexaflexagons erman traverse, will bring up the six faces of a hexahexa. I uploaded this on october 21, which is the birthday of martin gardner, the man who made hexaflexagons popular. How to make a hexahexaflexagon geometric toys to make aunt. Enter image locations in the six boxes below and hit one of the create buttons. The patreon is almost at the level of sustainability for me, though not quite, so i decided to do something new and sell shirts this month. The wikihow video team also followed the articles instructions, and validated that they work. Hexahexaflexagon template a3 captain musick air scouts.
To create this article, 19 people, some anonymous, worked to edit and improve it over time. How to make a hexahexaflexagon step 7 fold the forth triangle from the right back. Flexagons are folded paper polygons that have the neat feature of changing colors as they are flexed. At any time only 2 sides are visible, but a hexahexaflexagon actually has six sides. Origami hexaflexagon tutorial how to make a hexaflexagon. Martin gardner heres a nice interview thanks to the dragon illusion cutout. Manual do mundo comunicacao ltda caixa postal 77795. Hexahexaflexagon is constructed by cutting a strip of paper so that it may be marked off in 19 triangles a. When the 60 degree angles are in the center, you have a flat. They were discovered by british mathematician arthur stone in 1939, when his work at harvard, with their us sized paper, led him to cut strips off his sheets of uk paper, and folding these strips into equilateral triangles led to the discovery of these fascinating. This model celebrates all hexaflexagons with 6 or less faces. Pdf template for a hexahexaflexagon that we followed successfully. Jan 26, 2016 interestingly, in a hexahexaflexagon, each of the colored faces can appear in two different orientations such that, if you were to draw a sixpointed a star at the center of your hexagon, it would sometimes appear around the center and sometimes around the outer edges.
In geometry, flexagons are flat models, usually constructed by folding strips of paper, that can. 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. A well folded model will flex very smoothly with well formed faces. Dec 26, 2019 wikihow is a wiki, similar to wikipedia, which means that many of our articles are cowritten by multiple authors.
I uploaded this on october 21, which is the birthday of martin gardner, the man. A hexahexaflexagon is a foldable paper polygon with six faces. Pick the patterns that you like the best and then print out the template. Origami tutorial geometric printable templates 45 ideas for 2019 printable pattern fortrihexaflexagon with. Hold the flexagon in two hands, looking down at the top face. Oct 21, 2012 this video will show you how to make your very own hexahexaflexagon. Make a red and yellow hexahexaflexagon by folding and gluing a multicoloured paper strip, following the algorithm. At the same time pinch to make three mountain folds. In some positions you will not be able to open the center.
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