If you’re not happy yet, try saying “Hexaflexagon” a few times. It’s a fun word.
I first discovered hexaflexagons as a teenager, loved them, made them obsessively for a few weeks, and then lost interest. But a few (several) weeks ago it was world Hexaflexagon Day, and out of the blue I realised that I wanted a hexaflexagon covered with snakes.
So I drew these snakes…
… and these snakes drew themselves
Aren’t they cute? Then I had to see what happened if the snakes were allowed have more than one head each, or if more then two snakes slithered in from each edge, so it turned into more of a hydra than it seemed at first which is why this is at least a month late. Anyway.
Hydras
I tried making a template for you to print and cut and snake away yourself, but it required mad precision in getting marks on two sides of the page to line up perfectly when you print double-sided, and since you might not even use A4, depending where you live, it all got awfully error-prone. But here’s how you do it. You make a hexaflexagon following any of the instructions you find online – here, f’rinstance – and also you cut or fold or otherwise engineer a strip of paper the same length as the edges of your triangles.
This piece of paper is how you make all the bodies line up (gosh that sentence sounded less like you’re a crazy murderer in my head… moving swiftly on!) so symmetry is important. Fold it in half to find the midpoint, and make a pair of marks roughly in the middle of each half. They don’t have to be exactly in the middle, but the two halves do have to be perfect mirror images of each other.
An important pink piece of paper
Instead of seeing your flexagon as six triangles, see it as three regular diamonds. Use your guide strip to mark along each edge.
The edges of the diamond are the overlappy ones; the middle is just a crease
Fill it with snakes! This is now my go-to piece of advice for every situation. It won’t always solve the problem but it will generally give you a new and more interesting problem instead.
Just wrap them around any way you like!
Repeat for the remaining two diamonds. Try to get an equal number of heads and tails in there, or your snakes risk looking a bit funny. Unless you’re doing hydras, in which case try to have a majority of heads. A hydra that just kept growing new tails would be a fairly crappy foe. Oh lordy, though, I’ve just thought – a hydra scorpion that kept growing more tails would be nightmarish indeed, wouldn’t it?
Then you just flex it around to flip between arrangements of snakes. You’ve got two more surfaces waiting inside to be snakified too – you can even make them wrap from one side to the next!
Who looks sillier, the green snake with two tails and no head or the blue snake with two heads and no tail?
But I should think most people who’ve heard that line have thought the same thing in response to it. It’s a bit dog-in-the-manger. Just because you’d rather not know why certain things are as they are, that’s no reason for everybody else to avoid thinking about them. For lots of people, understanding how something came about is a gain, not a loss. (Richard Dawkins spent a whole book saying so, and it’s rather a good read.) 
Mostly Modular 