Today, Soul will be introducing you to one part of mathematics, which normally isn't taught in schools — you will learn how to create your very own hexaflexagon, a 6-sided figure which can be flexed numerous times (hence the name ^^) And everything you will need is a printer, scissors and glue.
Before we start a BIG Thank you goes to vihart from Youtube, without whose videos this wicket would not exist, and to cybie and Piper from TRForge, who allowed me to use their great wallpapers.
Template
Download one of the templates below (you can choose between DOC, PDF and JPG)
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Now let's start!
Print the template out.
Cut the two parts out. (Take your time and do it as exact as possible.)
Fold both stripes in the middle — a ruler may come in handy here.
Unfold the stripes again and glue them together…
…so that you now have ONE long stripe.
Fold it in half (thanks to the third step this should be rather easy) and glue the inner sides together.
Soon after you finally have the actual hexaflexagon-starting product in front of you: A long, thin stripe of paper which is composed of multiple equilateral triangles and printed double-sided.
Make sure that the second side points upwards and then fold it along every single black line. The easiest way to do that is to always fold the leftmost triangle onto the stripe, as it's shown in the pictures below.
At the end it should look like this:
Unfold it again, try smoothening it and then place it like this in front of you:
Now you have to shorten this long stripe by folding it in a special way, which is depicted step by step below:
Start by folding the first two triangles backwards.
(Check the picture below to see if you did it right)
Fold the right part of the stripe along the marked line.
Repeat steps a) and b) mutliple times…
… and you should soon have a smaller stripe, which is basically the long stripe in shape of a flat spiral.
Now you only have to fold it into the hexagon.
First fold it two times, as shown in the pictures (which are basically self-explanating)…
… and then move the right end BELOW the left end.
Finally just glue the two numbered triangles together - et voilá: You're done and can try out your very own TR-hexaflexagon! :-D
Now, what's so special about it?
At the moment your hexaflexagon should look just like in the photo above but that's only 6 of the 36 triangles from the beginning (remember the long stripe of paper?) Indeed you can “transform” it into another hexagon, so let's see how to do that:
Fold the hexagon into a threepronged star, by joining every second corner point (marked blue in the picture) in the middle.
Unfold this star again, but do that, by moving its centre apart (have a look at the picture below, to understand, what this means) and see what happens :)
You just unveiled your first hidden picture und can now repeat steps 1 and 2 numerous times and try to find other ones :)
Please note: Depending which corner points (there are two possibilities!) form the centre of your star you get other results, when you unfold it again. Sometimes only one of the possibilities work, which means, that it's perfectly normal, if you can't unfold the star.
Have fun experimenting with your new toy!
If you want to publish this text or parts of it elsewhere, please ask Soul for permission previously!
As every year there is also the TRForge advent calendar contest. Achieve the matching challenge to every calendar door and collect points, to get the chance to win a great prize in the end! You can find more infos here: contest, or you can click on Lara at the calendar page.