Hexaflexagons-- they're cool, hip, and hexa-fun
to play with, right?
Hexaflexagons are not toys.
With the increasing number of hexaflexagons finding their way
into homes and schools, it's important to be aware
of proper flexagation regulations
when engaging in flexagon construction and use.
Taking proper precautions can help avoid a flexa-catastrophe.
Do not wear loose clothing when engaging in flexagation.
If you have long hair, tie it back,
so it doesn't get caught in a flexagation device.
Ties are also a common source of incidents.
Never flexagate while under the influence.
When using a hexaflexagon, sudden unexpected sides
may appear, and drugs like alcohol can slow reaction time.
If you aren't sure what kind of flexagon you're dealing with,
it's safer to temporarily disable the flexagon.
Flexagons can be disarmed by using scissors
to cut them apart.
You can cut across the original seam
where the paper strip was taped together,
which may appear on the edge or through the face
of the flexagon.
In an emergency, however, flexagons
can be cut apart right through a triangle, or on three edges
if you want to retain symmetry, or into nine separate triangles
if you really want to be safe.
You can even cut them in half down the length of the paper
strip like this, into two separate--
Once you cut your flexagon apart,
you can figure out what kind it is.
If it has nine triangles, that's 18 triangle sides.
So at six triangles per hexagon side,
that's three sides of trihexaflexagon.
Note that some flexagons might be
made from a double strip of triangles that have been folded
in half, so that marker doesn't bleed through.
Don't let yourself be fooled by the extra triangles.
Avoid danger during hexaflexagon construction.
If you're not working from a printed pattern,
you might start your flexagon by picking a point
on the edge of a strip of paper, folding that 180 degree
angle into thirds to create 360 degree angles,
and then using the equilateral triangle that results
as a guide to fold the rest of the strip of paper,
zigzagging back and forth.
Without proper attention and focus,
this could easily lead to becoming unreasonably amused
with the springy spring of happy triangles that results.
Always keep your hexaflexagon in good working order.
Pre-creasing all the triangles both ways
before configuring them into hexaflexagonal formation
will help your flexagon operate properly and avoid accidents.
Keep a close watch on the chirality of your hexaflexagon.
That is, whether it is right or left handed.
Notice how in this hexaflexagon, water flows
clockwise down under the flaps, even
if you flip it over or flex it.
Well, in this hexaflexagon, it flows counter-clockwise.
They're mirror images.
The chirality is decided when you fold and tape
your triangles into a twisty loop, and once taped,
it is impossible to change from one
to the other without cutting it apart,
at least in three-dimensional euclidean space.
A change in chirality could be a sign
that your flexagon has been flipped
through four-dimensional space and is possibly a highly
dangerous multi-dimensional portal.
With experience, a hexaflexagon master
can construct a hexaflexagon in mere seconds.
Some forgo tape and scissors entirely
by folding a double strip that's too long
and tucking the extra in.
This is an advanced technique that should not
be attempted without prior training.
Beware topological changes.
This family seems safe from this philosoraptor,
because they live on separate planets
with a cold, empty vacuum of space between them.
But after a single flex, the unfortunate victims
are now doomed, protected only by the inconsequential barrier
of their domicile.
Your stars might explode, your frowns may become smiles,
your most pointy of triangles might
become the roundest of circles.
Perfectly healthy snakes may turn into snake loops,
or worse, become decapitated.
Either state is fatal for the snake,
as having no head can lead to starvation.
This can be avoided by simply marking where connections will
be across neighboring triangles first.
Afterwards, the lines can be filled in however you like.
Be aware that with the trihexaflexagon,
there are two variations to each face.
So you can simply draw one side where triangles connect,
and flip and draw the other.
But in the hexa-hexaflexagon, the main three
faces each appear four different ways.
If you use hexaflexagons, keep an eye
out for signs of dependency.
Overuse can lead to addiction and possibly an overdose.
Some users of hexaflexagons report confusion,
mind-blown syndrome, hexaflexaperplexia,
If you find yourself experiencing
any of these symptoms, stop flexagon use immediately,
and see the head of your math department.
With proper precautions, flexagating
can be a great part of your life.
Follow these simple safety guidelines,
and you should be ready for a fun and safe hexaflexagon