Another outrageous invention.

The Time-Twisting Trihexaflexagon

Dmitri gave me a tough assignment this time but I managed to track down something that does exactly what he needs, and so I bring you … the Time-Twisting Trihexaflexagon!

Since this is complicated science, let's take things very, very slow. First let us just build the trihexaflexagon. To do this, you need nothing but a piece of paper, scissors (or a single scissor if you can swing it) and a pot of glue. First copy the design of Figure 1 onto your paper:

You need ten equilateral triangles arranged in a line exactly like that. Be very careful with your measurements: the angles all must be 60 degrees and the sides all exactly the same length. I've used a side length of 2 inches for mine, making the entire strip 11" long. (If you don’t want to do all the measuring and calculating, you can print my design on a piece of paper and just cut it out.) Trace the triangles onto the back side as well, making sure they correspond with those on the front as perfectly as you can manage. Then turn the paper back over so it again looks as in Figure 1. Now number the triangles exactly like that. Next, turn the paper upside down again (flipping it bottom to top rather than turning it over from left to right), and number the triangles on the other side as in Figure 2:

Note that the two triangles on the ends are now marked X, so that you only have 8 triangles left which are marked 1, 2 or 3.

From here, make the first fold. Fold the paper AWAY FROM YOU at the line between the pair of 3's and the pair of 1's. Make sure you fold exactly on the line. Your paper should now look as in Figure 3:

The next fold is between the next pair of 3's and the pair of 1's that now face you, again folding the paper away from you. You should now see something looking like Figure 4:

You'll now have something almost hexagonal with almost all-3's on the side facing you. Make it completely so by tucking the end of the strip over so that the final x overlaps the 2 and lies right next to the initial x, as in Figure 5:

Coat one or both x's with glue. Now fold the initial x in onto the final x, pasting the two together (make sure you ONLY paste these two faces together and none of the rest of the strip). And that's it! Now you have a flexagon! The side you’re seeing now has six triangles all marked 3, as in Figure 6:

If you turn the flexagon over, you'll see that on the other side, all the triangles are marked 1, as in figure 7:

So what happened to all the triangles marked 2? They are now inside the flexagon, of course. You've folded them in, and then you sealed their fate by gluing the x’s together so they're now trapped in there forever. Right?

Well, that's where the magic comes in. Prepare your flexagon for easy flexing by folding it both backward AND forward along each of the three corner-to-corner lines that run through the centre. Now carefully study Figure 8, the guide to flexing the flexagon:

Start by holding the flexagon with the side marked 1 facing you. Take note of where the open slits are, inside of which, if you peek in, you can see the side marked 2 hiding. The next part is impossible to convey in any human language so just look at the pictures and try to do what the hands in the illustration are doing. If you manage it, you'll miraculously discover that you've turned the flexagon inside-out without ripping it, and you're now looking at the side marked 2! You’ll see the side marked 1, the one that faced you at the start, is now at the back of it. But the side marked 3 has disappeared! Indeed if you peek in at one of the slits, you'll see that side 3 is now tucked away on the inside! If you repeat the same complicated flexing procedure, you'll end up faced with the side marked 3, the side marked 2 on the back, and side 1 now hidden on the inside. A final flexing will again restore the flexagon to its original state, with side 1 facing you, side 3 on the back and side 2 on the inside.

THE SCIENCE

This is the first part of our project. You now have a working flexagon! But what is the science behind it? Well, the great discovery of our age is that the flexagon works by actually twisting space and time. Admit it! You can’t figure out how it could conceivably be possible to turn it inside out and partially back to front, even while you’re doing it. The geometry just doesn’t make any sense! What exhaustive investigation down to the nano-level has revealed, is that the triangles actually move through a fourth spatial dimension and rearrange themselves as you're flexing the flexagon. Not only that! There is a simultaneous effect that twists time itself. It is a very small effect, and yet you notice it while you're flexing your flexagon and trying to work out what is going on with it. The more you concentrate on it, the less you are aware of the passage of time. Intense concentration will even make you feel as if time itself briefly stops. It turns out, time really DOES stop! But just briefly.

This is what science has discovered … and of course the next thought was, what a waste! What's the point of being able to alter space and time just for a few minutes of puzzlement fiddling around with a stupid piece of paper? So of course science tackled the project of weap … I mean of gaining some actually practical use out of the flexagon. The breakthrough was made by Professor Suna Bloma of the University of Estonia. She found that coating the flexagon in three different compounds remarkably enhances the effect. The first is simple tinfoil. This has already been proven to have outstanding insulating effects on the very subtle psi-field. The next is a special piezoelectrical silicon crystal lattice Bloma calls 'quantum pixel filaments'. The last is a sticky substance that Bloma claims attracts and captures extremely subtle sub-atomic particle complexes she whimsically dubbed 'fairies' (and paper coated with the substance being equally-whimsically called 'fairy flypaper'). These last two, though entirely new inventions, are nevertheless cheap and easy to manufacture and store, which is good since the physics department of the university of Estonia has a bare-bones budget. You can actually order them from the university … please do so! You may need to wait a few months for them to arrive, but once they do, waiting will not be a problem in your life ever again.

Good, so now you have your quantum pixels and your fairy glue. I trust you can get tin foil without a problem. Take your flexagon. Start with the face marked 1. Paste a small patch of tinfoil in the middle of each of the six triangles. Flex the flexagon to show you face 2. Spray on a thin layer of quantum pixels with the special spraycan. Flex the flexagon to show face 3. Using a thin paintbrush, apply a dab of fairy glue right in the centre of each triangle. Now the flexagon is activated! Next – you need to activate YOURSELF! Draw a triangle on your forehead. Put a patch of tinfoil at the apex of the triangle, spray some quantum pixels on the lower right corner and put a dab of fairy glue on the lower left corner. Now you're attuned!

Take the flexagon again. Now, thanks to these miraculous compounds, flexing it will actually fold time and space for you! To commit a bit of technobabble: you actually are visiting alternative versions of reality itself, only very, very minutely different from ours, so everything seems the same to you as the world you know … but you can jump to what seems to you to be quite different times and places, and you will find there a body quite closely corresponding to your own to receive you! This only works for times within your own lifetime or potential lifetimes, and for places you could realistically visit in those alternate realities. But you will always find yourself with the time twister still in your hands, so you can travel even further from there. The three compounds the faces are covered in are used to pinpoint your destination: the tinfoil will take you to a time and place of suspense and adventure; the quantum pixels will take you to a time and place of peace and relaxation; the fairy glue will take you to a time and place of joy and wonder. The first turn will take you to the closest such situation in all of virtual spacetime; the next turn will take you to the one after that, and so on. You can go forward in time by twisting the flexagon forward, that is to say from face 1 to face 2 to face 3 and repeat; twisting the opposite way will take you backwards in time. Breaking contact, by wiping your forehead, will return you to the 'real' present. But experiment with it, to find out just how it will work for you! Though it doesn’t alter 'real' reality, you can have a most satisfying respite from it whenever you want! It's just beyond awesome!

POSTSCRIPT

I am saddened to inform you that the University of Estonia no longer supplies the fairy glue or the quantum pixels! If I had known this would happen, I would have guarded my own supply … I'm afraid I've gone wild with it and I have none left! Anyways it's a real calamity. From what I've been able to discover, there were … tensions at the university. Now this is the best I can figure it out: Professor Bloma had a superior, Doctor Skoba Jako. Behind her back he tried patenting both compounds and making a deal with a huge American corporation, who were planning to either sell it at an exorbitant price or hold it back while trying to work out how they can use it for other profitable endeavours. But it was at any rate not something that sat easy with Prof. Bloma, who believed the benefit should go free to all of humanity. Unfortunately the rest of the physics staff at the university would not back her up, the talk being that they needed the money. What happened next is hard to puzzle out. There was some sort of scene at the lab … there are people who think they remember witnessing it … some people remember Bloma finally shouting some not very polite words at Jako, and then taking out something from her pocket. She unfolded it … kept unfolding it; it grew larger and larger and everyone was dumbfounded. Then, after a final insult, she … folded herself into it; there was one final kind of folding happening, stranger than anything any of the witnesses ever had seen, and then she was gone. Just gone, along with the strange device.

And what's more … all samples, all documentation, all records, everything related to the compounds and the project … gone! There was nothing whatsoever left. Skoba Jako in his consternation found that he could remember nothing about the compounds; he had not the faintest glimmer of a clue how to recreate them. The corporation he was making deals with had received no physical samples and was now accusing him of fraud. And what’s more … Bloma herself completely vanished from the university's files and records! There was nothing whatsoever left, nothing to prove she had ever been connected to the university! Indeed, according to all records and documents in the entire country, she just vanished, for all intents and appearances right off the face of the earth, fifteen years ago! No trace of her existence after that … except for her elderly father, the only surviving family she has, who swears high and low that his daughter has never stopped visiting him, popping in at least twice a year, and that she looks healthy and exceedingly happy. But the father is, and has been for all that time, institutionalized for dementia …

Memories simply don't stack up to official documentation. The university ultimately had no choice but to conclude that Bloma never was connected with it; just HOW all those other people came to imagine this person, this person who went missing in unknown circumstances a decade and a half ago, as having been there and doing all that research, they have yet to explain. But there has to be an explanation … right?

So I am dreadfully sad to disappoint everyone … without those miracle compounds, the time twister just doesn't work, except on its minimal 'base'-level. I don't know if anyone in the world has any left, I think they only ever sent it out to a few people, and if they were as careless with their supplies as I was … But who knows … someday, perhaps someday soon, Bloma might return!

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Willem

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