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PROFESSOR: All right.

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So today we resume
efficient origami design.

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And we had our guest
lecture from Jason Ku

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which was definitely a
different style of lecture.

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More survey, lots of
different artwork.

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And it had some practical
hands-on experience

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with TreeMaker, which
you're welcome to do

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more of on your problem set.

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And so there weren't
a lot of questions

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because this is not a
very technical lecture,

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so I thought I'd
show you some more

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examples of artistic origami,
things not covered by Jason,

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and some other different
types of origami.

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So we start with a
bunch of models by Jason

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because he didn't
show his own models,

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so I thought it'd be fun.

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We've seen a bunch
already in this class,

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but this is a really nice
F16 that he designed.

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And these are all done with
Tree method of origami design.

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Another lobster.

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We saw a Robert
Lang's lobster before.

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This one's different.

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This is a version of
the crab that he showed.

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So the one you saw was like the
very preliminary, very rough

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folding.

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But with some
refinement, especially

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in the shaping stage,
it looks pretty nice.

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Even on the back side you
get some nice features.

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We have a little rabbit.

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This is kind of in
the traditional style

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that he showed where you've
got sharp crease lines that

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really define the form.

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I assume that's what
he was going for here.

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This is a non-tree
method design.

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This is using what's
called box pleating.

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We've heard about box pleating.

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And it means you have
horizontal, vertical,

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and 45 degree diagonal folds.

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But you can use it just
to shape box-like shapes.

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It originally was used by
Moser to make a train out

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of one rectangle of paper.

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But here we've got a pretty
nice sports car convertible,

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even with a color reversal.

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So it's pretty cool.

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This is one of my favorite
designs of Jason's.

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Bicycle, one square
paper, color reversal.

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Really thin features.

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Probably lots of layers up
there, but pretty awesome.

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This is using tree method.

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Obviously, the paper is
not connected with a hole

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there, so there's
some part here that's

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attached just by
folding to another part.

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Yeah, questions?

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AUDIENCE: How big is that?

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PROFESSOR: I'm
trying to remember.

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I think the bicycle's
about that big.

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Anyone remember?

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It's been a while.

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So presuming he started
from a piece of paper

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maybe twice the size or so.

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Looks big here.

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And this is a really complicated
butterfly, very exact features,

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very cool.

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These are all from his website
if you want to check out that.

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I'm just giving a selection.

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Some of them have
crease patterns

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and you can very clearly
see the different parts

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of the model, and the
rivers, and so on.

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Others do not.

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This is one of-- we're
going back in time, so this

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is when Jason was just starting
at MIT as an undergrad,

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I believe.

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This is the dog of someone who
works at the admissions office.

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It's very cool.

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And this is one of his
earliest models, 2004.

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I think it's pretty
elegant on the ice

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skate with color reversal.

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So that was Jason, for fun.

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One question we had
is what about origami

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from other materials,
not just paper?

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And we've seen a few
examples of that,

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but I thought it'd
be a fun theme.

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And we'll come back to
this a couple times today.

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This is-- I don't if you
call dollar bills paper--

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but there is this whole
style of dollar bill origami,

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as my t-shirt last
class indicated.

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And this is one of the more
famous dollar bill folders.

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And he has hundreds and
hundreds of designs.

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One of his latest is the alien
face hugger for Prometheus

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and so on.

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So there's a ton of stuff done.

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There's the
particular proportion

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of the rectangle
of a dollar bill.

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And it's also just
plentily available.

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The US is one of the
cheapest currencies

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to do bill folding because it
has one of the lowest value

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bills.

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So there's that.

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These are all folded
from toilet paper rolls,

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so moving up to cardboard.

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This definitely is pretty
different in the way

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it acts relative
to standard paper.

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And there's this guy who
makes these incredible masks.

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Very impressive.

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And I'm guessing crayon or
some kind of rubbed color.

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So that's pretty awesome.

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Here's something
called Hydro-Fold.

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This just came out this year
by this guy Christophe Guberan,

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where he's got an
inkjet printer.

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He's filled it with a
particular kind of ink

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that he custom makes.

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And as it comes out of the
printer, it folds itself.

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It's been printed on both sides.

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So one side you get mountains,
the other side you get also

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mountains, but relative
to that, it's valleys.

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So there's some
fun thing happening

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as the liquid dries out that
causes the paper to curve.

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You can't get 180
degree folds, but you

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can get some pretty
nice creases.

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I don't know exactly how
much accelerated that is,

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but he's hopefully
visiting MIT later on

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and we'll find out more.

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So it's using regular paper,
but a different folding style,

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a different material
for folding.

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You can also take casts
of existing paper models.

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So Robert Lang has
done a bunch of these

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with a guy named Kevin Box
where they take a paper model

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and cast or partially cast it.

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In this case, in bronze.

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In these cases, stainless steel.

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So these are two.

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This is like traditional
origami crane and Robert Lang

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complex crane.

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And for fun, the crease pattern
for those two looks like this.

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And this is I think mostly
on a 22.5 degree grid system.

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May actually be--
you can see here

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there's a river
that's not orthogonal.

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So it's not intended
to be box pleated.

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So that gives you
these 22.5 degrees.

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There's some other features
out here, but the most of it

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is this 22.5 degree system.

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So as you might guess
from now, there's

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some questions about this.

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You don't necessarily
entirely use the tree method.

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You use a mix of
different things.

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In particular,
there's a technique

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called grafting where you
can combine two models.

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If you're interested
in that, check out

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Origami Design Secrets.

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And for things like
the dragon where

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you have this textured
pattern-- which we'll get to,

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it's called a
tessellation-- and you

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want to combine that with
doing tree method stuff,

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you can do that.

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But it's not necessarily
mathematical formal

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how to do that.

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It's just people figure
it out by trial and error.

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There's probably
interesting open problems

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there, haven't been formalized.

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Here's another cardboard design.

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This is by our friend
Tomohiro Tachi.

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That's him.

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So this was initially a bed.

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And you fold it up.

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And you need a
pillow, of course.

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It turns into a chair.

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So that's pretty awesome.

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So that's one of
the great things

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about using non-paper is you get
a lot more structural integrity

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and support.

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And that leads us
into steel, which

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also makes for stronger models.

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And this is another
design by Tomohiro.

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We made it here at MIT using
a waterjet cutter in CSAIL.

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And it makes a
pretty nice table.

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This is based on a curve crease
design which initially drafted

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on paper, and then in plastic.

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And then when it seemed
to be working pretty well,

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we waterjet cut this steel
and these perforation lines.

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And then many hours of painful
bending or difficult bending

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later, some hamming
and so on, we

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got it to fold into
a pretty nice shape.

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So that's one example.

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I have another example.

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This is out of
much thinner steel.

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And this happens to be laser
cut using a newer laser

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cutter in the Center for Bits
and Atoms in the Media Lab

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building.

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So a little bit of a cheat.

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This is not from a square paper.

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It's been cut a
little bit smaller.

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I need chalk.

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Jason.

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So take a square of paper.

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You can cut out-- these
are 22.5 degree angles.

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You can cut out material
like this from your square

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and still make a good crane.

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But it substantially
reduces the number

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of layers you get,
especially at the corners.

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And so we exploited that because
this is pretty thick material.

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And this is just the Center
for Bits and Atoms logo.

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But pretty cool.

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You can make a crane.

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And we added these
crease lines to get

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the nice bow of the crane.

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So pretty nice.

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This is made by Kenny Cheung
who just graduated, PhD.

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So that was some metal.

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Next topic is tessellations.

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So this is a particular
style of origami.

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It goes back-- probably
the earliest tessellation

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folder is Ron Resch.

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The early history's a little
hard to know for sure.

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Ron Resch was an artist
starting in the '60s.

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He died just a few years ago.

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We've met him.

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Pretty crazy guy.

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Did a lot of cool origami
foldings early in the day.

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There's a patent that describes
this particular folding.

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And what makes a
tessellation is essentially

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a repeated pattern of some sort.

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It could be periodic.

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It could be aperiodic.

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You've probably heard
of tessellations

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like the square grid or some
kind of mesh of two dimensions.

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Origami tessellations
are in some sense

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trying to represent
such a tessellation.

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Here you've got the
triangular grid,

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if you look closely,
after folding.

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But also if you look at
the crease pattern itself,

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it is a tessellation.

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It's going to be a repeated
pattern of polygons.

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So you've got sort of two
levels of tessellation going on.

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It's like a double
rainbow or something.

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And so there are lots
of examples of this.

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Here's some kind of traditional
flat origami tessellations.

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Some of these are more
traditional than others.

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You've some very simple--
well not simple, but beautiful

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repeating patterns.

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Octagons and squares here.

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You can count them.

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And this is still periodic.

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Then we get to some
less periodic stuff.

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And so there are
techniques for designing

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these kinds of tessellation.

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If you start with a
regular 2D tessellation,

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there's a transformation
from that tessellation

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into a crease pattern, which
then makes things like this.

258
00:11:42,620 --> 00:11:46,120
You can see here there's
sort of clear edges here.

259
00:11:46,120 --> 00:11:49,400
And that represents the
tessellation it's based on.

260
00:11:49,400 --> 00:11:51,310
It's just been kind of
shrunk a little bit.

261
00:11:51,310 --> 00:11:52,580
Each of these is a pleat.

262
00:11:52,580 --> 00:11:54,990
There's a mountain
and a valley crease.

263
00:11:54,990 --> 00:11:58,500
And so on all of these,
I believe, that style.

264
00:11:58,500 --> 00:12:02,800
You've got essentially a twist
fold at each of the vertices.

265
00:12:02,800 --> 00:12:07,122
And you've got a pleat
along each of the edges.

266
00:12:07,122 --> 00:12:08,580
And if you want to
play with these,

267
00:12:08,580 --> 00:12:12,700
there's software called Tess
freely available online.

268
00:12:12,700 --> 00:12:14,210
And I'll show it to you.

269
00:12:14,210 --> 00:12:19,760
And it lets you design
things like this,

270
00:12:19,760 --> 00:12:22,430
following a
particular algorithm.

271
00:12:22,430 --> 00:12:24,280
So you start with some geometry.

272
00:12:24,280 --> 00:12:27,190
And I don't really
know these by heart.

273
00:12:27,190 --> 00:12:29,605
So it has a fixed
set of geometries

274
00:12:29,605 --> 00:12:31,580
that you can play with.

275
00:12:31,580 --> 00:12:34,020
We'll try this one.

276
00:12:34,020 --> 00:12:40,300
And you get a regular 2D
tessellation of polygons.

277
00:12:40,300 --> 00:12:46,585
And then you increase the--
then I hit, Show Creases.

278
00:12:46,585 --> 00:12:49,850

279
00:12:49,850 --> 00:12:51,670
And it's applying a
particular algorithm

280
00:12:51,670 --> 00:12:54,430
which is essentially-- it's
maybe more dramatic if I

281
00:12:54,430 --> 00:12:58,230
increase this value or
change it dynamically.

282
00:12:58,230 --> 00:13:02,410
It's rotating each of the
polygons, so a twisting.

283
00:13:02,410 --> 00:13:04,710
Sorry, that's negative.

284
00:13:04,710 --> 00:13:09,100
As it rotates them, you
get-- let me know you.

285
00:13:09,100 --> 00:13:11,280
It'd be nice if this is
color-coded, but it's not.

286
00:13:11,280 --> 00:13:13,650
So these two squares
are two original squares

287
00:13:13,650 --> 00:13:14,900
of the tessellation.

288
00:13:14,900 --> 00:13:16,120
They've been twisted.

289
00:13:16,120 --> 00:13:18,350
And then these edges
which used to be--

290
00:13:18,350 --> 00:13:20,690
so they're shrunk and twisted.

291
00:13:20,690 --> 00:13:22,820
And then these edges
used to be attached.

292
00:13:22,820 --> 00:13:26,870
We're now going to put in a
little parallelogram there.

293
00:13:26,870 --> 00:13:28,492
And you just do that everywhere.

294
00:13:28,492 --> 00:13:29,700
And this is a crease pattern.

295
00:13:29,700 --> 00:13:31,140
It will fold flat.

296
00:13:31,140 --> 00:13:32,640
Doesn't work for
all tessellation.

297
00:13:32,640 --> 00:13:34,070
And there's a paper
characterizing

298
00:13:34,070 --> 00:13:35,445
which tessellations
it works for.

299
00:13:35,445 --> 00:13:37,210
They're called spider webs.

300
00:13:37,210 --> 00:13:38,940
But it's a very simple
algorithm and it's

301
00:13:38,940 --> 00:13:41,360
led to tons of tessellations
over the years.

302
00:13:41,360 --> 00:13:46,050
And you can export this to
PDF, print it out, and fold it.

303
00:13:46,050 --> 00:13:47,620
It obviously takes
a little while.

304
00:13:47,620 --> 00:13:50,660
One of the fun surprises
of this algorithm, which

305
00:13:50,660 --> 00:13:52,320
this is made by Alex
Bateman and this

306
00:13:52,320 --> 00:13:54,440
was just sort of a
surprise by accident.

307
00:13:54,440 --> 00:13:57,920
I think there's a slider at the
top, the pleat angle slider.

308
00:13:57,920 --> 00:14:02,350
And by accident, he didn't
require it to be positive.

309
00:14:02,350 --> 00:14:05,350
And he realized that if you
made it negative-- whoa, that's

310
00:14:05,350 --> 00:14:11,120
a little too negative-- you
actually get the folded state.

311
00:14:11,120 --> 00:14:13,730
This is what that
crease pattern will

312
00:14:13,730 --> 00:14:16,380
look like after you fold it
flat, because it's essentially

313
00:14:16,380 --> 00:14:19,100
reflecting across each crease.

314
00:14:19,100 --> 00:14:21,950
So this is with all
the layers stacked up.

315
00:14:21,950 --> 00:14:23,900
So you get sort
of an x-ray view.

316
00:14:23,900 --> 00:14:25,660
But it gives you
a sense of-- it's

317
00:14:25,660 --> 00:14:28,020
hard to see the thickness
here so we actually wrote

318
00:14:28,020 --> 00:14:33,040
a little thing here which
is a little bit slow--

319
00:14:33,040 --> 00:14:36,211
we'll see if it works--
called Light Pattern.

320
00:14:36,211 --> 00:14:38,460
And it's just measuring how
many layers are stacked up

321
00:14:38,460 --> 00:14:41,250
at each point and
it will hopefully

322
00:14:41,250 --> 00:14:44,180
give you a shaded pattern
so that if you held it up

323
00:14:44,180 --> 00:14:46,891
to light where the dark
spot's going to be,

324
00:14:46,891 --> 00:14:48,390
where the bright
spot's going to be.

325
00:14:48,390 --> 00:14:50,400
So the idea is this
will help you figure out

326
00:14:50,400 --> 00:14:52,984
whether something's going to be
interesting or not interesting

327
00:14:52,984 --> 00:14:53,775
ahead of have time.

328
00:14:53,775 --> 00:14:56,290
Then you can go fold once you've
set the parameters exactly

329
00:14:56,290 --> 00:14:57,290
like you like.

330
00:14:57,290 --> 00:14:59,230
I've just shown one of
the parameters there.

331
00:14:59,230 --> 00:15:02,770
There's another
one, pleat ratio.

332
00:15:02,770 --> 00:15:03,620
So this is cool.

333
00:15:03,620 --> 00:15:06,120
I think an interesting project
would be to extend this tool.

334
00:15:06,120 --> 00:15:08,090
It's open source.

335
00:15:08,090 --> 00:15:09,960
Lots of interesting
things to do with it.

336
00:15:09,960 --> 00:15:11,190
Add more tessellations.

337
00:15:11,190 --> 00:15:13,750
Improve the interface.

338
00:15:13,750 --> 00:15:17,130
Maybe try to show 3D
visualization as it folds.

339
00:15:17,130 --> 00:15:19,460
There are existing
3D origami tools

340
00:15:19,460 --> 00:15:21,770
which we'll see in the very
next lecture, Rigid Origami

341
00:15:21,770 --> 00:15:25,130
Simulator, that might make
that not too hard actually.

342
00:15:25,130 --> 00:15:28,202
It'd be cool to try.

343
00:15:28,202 --> 00:15:30,160
Put it on the web I think
would be interesting.

344
00:15:30,160 --> 00:15:32,111
Point it to JavaScript
or something.

345
00:15:32,111 --> 00:15:34,360
Because I think there's
really cool tessellation here.

346
00:15:34,360 --> 00:15:37,610
Not many people have
actually used the software

347
00:15:37,610 --> 00:15:41,910
because it's a little
awkward and as you can see,

348
00:15:41,910 --> 00:15:43,380
Light pattern
doesn't always work.

349
00:15:43,380 --> 00:15:45,504
But I think that's just
because this tessellation's

350
00:15:45,504 --> 00:15:47,491
a little too big.

351
00:15:47,491 --> 00:15:47,990
All right.

352
00:15:47,990 --> 00:15:50,330
So that was Tess.

353
00:15:50,330 --> 00:15:52,150
And that style of tessellation.

354
00:15:52,150 --> 00:15:54,233
You can see that you could
some really cool thing.

355
00:15:54,233 --> 00:15:56,640
This is what a light
pattern looks like.

356
00:15:56,640 --> 00:16:00,430
So you get the different
shades of gray.

357
00:16:00,430 --> 00:16:01,310
50 shades of gray?

358
00:16:01,310 --> 00:16:04,640

359
00:16:04,640 --> 00:16:06,890
Then there are more three
dimensional tessellations.

360
00:16:06,890 --> 00:16:10,430
So this is in a different style.

361
00:16:10,430 --> 00:16:15,380
And this is folding
a very simple origami

362
00:16:15,380 --> 00:16:17,730
base called water bomb.

363
00:16:17,730 --> 00:16:21,300
And the resulting
thing is not flat,

364
00:16:21,300 --> 00:16:23,080
but it's very simple
crease pattern

365
00:16:23,080 --> 00:16:24,890
and pretty cool three
dimensional result.

366
00:16:24,890 --> 00:16:26,190
This is not captured by Tess.

367
00:16:26,190 --> 00:16:27,981
And that would be a
different style project

368
00:16:27,981 --> 00:16:30,585
to generalize to
3D tessellations.

369
00:16:30,585 --> 00:16:32,400
That'd be very cool.

370
00:16:32,400 --> 00:16:38,350
Here's that same tessellation,
I think, or a very similar one,

371
00:16:38,350 --> 00:16:41,090
but made out of stainless steel.

372
00:16:41,090 --> 00:16:44,180
So you can see
there's big cuts here.

373
00:16:44,180 --> 00:16:47,030
So this is probably made
on a waterjet cutter.

374
00:16:47,030 --> 00:16:49,630
And then you leave little tabs.

375
00:16:49,630 --> 00:16:52,910
So you wear gloves so you
can fold this by hand.

376
00:16:52,910 --> 00:16:57,320
Probably not easy, but possible.

377
00:16:57,320 --> 00:17:01,149
Here's some more back to paper,
some more 3D tessellations.

378
00:17:01,149 --> 00:17:03,440
And if you're interested in
playing with tessellations,

379
00:17:03,440 --> 00:17:04,619
you could try Tess.

380
00:17:04,619 --> 00:17:08,160
Or there's this really
good book came out recently

381
00:17:08,160 --> 00:17:11,040
by Eric Gjerde,
Origami Tessellations.

382
00:17:11,040 --> 00:17:13,160
And this is actually
one of the models

383
00:17:13,160 --> 00:17:16,140
that's described in here.

384
00:17:16,140 --> 00:17:19,250
Unlike traditional origami,
there's no sequence of steps.

385
00:17:19,250 --> 00:17:21,930
All of these are based on
here's a crease pattern,

386
00:17:21,930 --> 00:17:23,560
fold along all the
lines, and then

387
00:17:23,560 --> 00:17:26,480
collapse all the
lines simultaneously.

388
00:17:26,480 --> 00:17:28,339
Like a lot of mathematical
origami design,

389
00:17:28,339 --> 00:17:30,684
but there's great stuff in here.

390
00:17:30,684 --> 00:17:32,100
Really cool
tessellations and some

391
00:17:32,100 --> 00:17:34,950
of the best photographs
of tessellations.

392
00:17:34,950 --> 00:17:36,580
So definitely
check out that book

393
00:17:36,580 --> 00:17:39,780
if you want to do tessellations.

394
00:17:39,780 --> 00:17:41,180
This is the crease pattern.

395
00:17:41,180 --> 00:17:43,750
Give you an idea for this guy.

396
00:17:43,750 --> 00:17:46,440

397
00:17:46,440 --> 00:17:48,600
It's also periodic.

398
00:17:48,600 --> 00:17:50,425
This is triangular twists.

399
00:17:50,425 --> 00:17:56,860
You can kind of recognize
that, but it's very cool.

400
00:17:56,860 --> 00:17:58,220
More alternate materials.

401
00:17:58,220 --> 00:17:59,920
This is polypropylene.

402
00:17:59,920 --> 00:18:02,060
And there's this
great Flickr site,

403
00:18:02,060 --> 00:18:04,200
polyscene by Polly Verity.

404
00:18:04,200 --> 00:18:08,130
And tons of examples of
foldings by polypropylene.

405
00:18:08,130 --> 00:18:10,050
So it's a kind of plastic.

406
00:18:10,050 --> 00:18:16,870
It gets scored by a machine
and then folded by hand.

407
00:18:16,870 --> 00:18:18,265
And so really striking results.

408
00:18:18,265 --> 00:18:19,765
You get this nice
semi-transparency.

409
00:18:19,765 --> 00:18:21,431
It works really well
with tessellations.

410
00:18:21,431 --> 00:18:24,500

411
00:18:24,500 --> 00:18:28,090
Here's some recent ones we
just found making things out

412
00:18:28,090 --> 00:18:35,100
of mirror and plywood and copper
as like the surface material,

413
00:18:35,100 --> 00:18:39,810
and then polyester and fabric,
or polyester and Tyvek.

414
00:18:39,810 --> 00:18:42,260
Tyvek is like those
envelopes, plasticy envelopes

415
00:18:42,260 --> 00:18:45,340
that you can't really
stretch or tear.

416
00:18:45,340 --> 00:18:46,410
Really great stuff.

417
00:18:46,410 --> 00:18:48,906
And you can buy it in sheets.

418
00:18:48,906 --> 00:18:50,530
So that's sort of
the base layer that's

419
00:18:50,530 --> 00:18:51,830
holding everything together.

420
00:18:51,830 --> 00:18:56,850
At the creases here, you can see
through to the fabric material.

421
00:18:56,850 --> 00:18:59,720
And then this is
plywood on the surface.

422
00:18:59,720 --> 00:19:01,684
So these are all
different tessellations,

423
00:19:01,684 --> 00:19:02,600
kind of tessellations.

424
00:19:02,600 --> 00:19:06,530
These have been wrapped
around to make vessels

425
00:19:06,530 --> 00:19:10,000
or to make-- they call
it a shoulder cape.

426
00:19:10,000 --> 00:19:12,000
Looks like a set of armor.

427
00:19:12,000 --> 00:19:16,650
But really cool stuff when
you work with other materials.

428
00:19:16,650 --> 00:19:18,630
It'd be a great project
in this class, I think,

429
00:19:18,630 --> 00:19:20,990
to try some of these techniques.

430
00:19:20,990 --> 00:19:24,764
Combining some basic
foldable sheet material

431
00:19:24,764 --> 00:19:26,180
with some richer
material, you can

432
00:19:26,180 --> 00:19:28,549
make some really cool stuff.

433
00:19:28,549 --> 00:19:30,090
Once you have a
computer model of it,

434
00:19:30,090 --> 00:19:33,749
you can-- and we'll
see in the next lecture

435
00:19:33,749 --> 00:19:36,040
different computer tools for
doing that-- then actually

436
00:19:36,040 --> 00:19:38,010
building them I think
is really striking.

437
00:19:38,010 --> 00:19:41,560

438
00:19:41,560 --> 00:19:44,160
Back to paper, although this
barely looks like paper.

439
00:19:44,160 --> 00:19:47,130
These are some really cool
kind of traditional style

440
00:19:47,130 --> 00:19:49,740
tessellations, but folded in a
very unusual and beautiful way

441
00:19:49,740 --> 00:19:54,826
by Joel Cooper who's one
of the leading tessellation

442
00:19:54,826 --> 00:19:55,950
folders in a certain sense.

443
00:19:55,950 --> 00:19:58,200
He's best known for
tessellations like this,

444
00:19:58,200 --> 00:19:59,230
however.

445
00:19:59,230 --> 00:20:01,770
So these are all based
on a regular triangular

446
00:20:01,770 --> 00:20:05,540
grid, but not quite identical.

447
00:20:05,540 --> 00:20:07,850
It's definitely
not periodic here.

448
00:20:07,850 --> 00:20:10,230
Going for human forms.

449
00:20:10,230 --> 00:20:12,460
He has whole busts and heads.

450
00:20:12,460 --> 00:20:15,097
And these are really striking.

451
00:20:15,097 --> 00:20:17,180
They're not designed
particularly algorithmically.

452
00:20:17,180 --> 00:20:20,310
My understanding is he
comes up with little gadgets

453
00:20:20,310 --> 00:20:23,480
for certain features
like cheeks and so on,

454
00:20:23,480 --> 00:20:26,880
and he starts composing them
in ways that seem to work.

455
00:20:26,880 --> 00:20:29,230
And he has a collection
of different pieces

456
00:20:29,230 --> 00:20:30,610
that work together well.

457
00:20:30,610 --> 00:20:33,140
And he can get really
intricate, really beautiful

458
00:20:33,140 --> 00:20:36,760
3D surfaces out of that.

459
00:20:36,760 --> 00:20:39,430
So this is kind of begging
to be studied mathematically

460
00:20:39,430 --> 00:20:41,180
in some way, but
pretty challenging.

461
00:20:41,180 --> 00:20:46,500

462
00:20:46,500 --> 00:20:49,850
This is an interesting
tessellation style

463
00:20:49,850 --> 00:20:51,370
by Goran Konjevod.

464
00:20:51,370 --> 00:20:54,540
He was a co-author on the
"Folding a Better Checkerboard"

465
00:20:54,540 --> 00:20:57,150
paper that I talked about.

466
00:20:57,150 --> 00:20:59,470
And the crease pattern
here is extremely boring.

467
00:20:59,470 --> 00:21:02,034
It's a square grid.

468
00:21:02,034 --> 00:21:03,450
But the mountain
valley assignment

469
00:21:03,450 --> 00:21:04,560
is not quite trivial.

470
00:21:04,560 --> 00:21:07,600
And because of the
thickness of the material,

471
00:21:07,600 --> 00:21:10,320
it actually gets this
curving behavior.

472
00:21:10,320 --> 00:21:15,060
So this thing is technically,
mathematically it's flat.

473
00:21:15,060 --> 00:21:18,390
It's like this really
boring pleated square.

474
00:21:18,390 --> 00:21:21,717
But the way it goes is
you sort of take a square

475
00:21:21,717 --> 00:21:23,800
and you pleat the edge and
then you pleat the edge

476
00:21:23,800 --> 00:21:24,758
and you pleat the edge.

477
00:21:24,758 --> 00:21:26,740
So you do mountain
valley, mountain valley.

478
00:21:26,740 --> 00:21:29,714
And here you're alternating
between this side and this side

479
00:21:29,714 --> 00:21:30,880
and this side and this side.

480
00:21:30,880 --> 00:21:33,150
And that gives you
this kind of corner.

481
00:21:33,150 --> 00:21:35,470
But because the material
is nonzero thickness,

482
00:21:35,470 --> 00:21:37,000
you get these
really cool curves.

483
00:21:37,000 --> 00:21:39,830
And when you change which
order you fold the pleats in,

484
00:21:39,830 --> 00:21:41,810
you can really control
a lot of this surface.

485
00:21:41,810 --> 00:21:42,800
It's kind of magical.

486
00:21:42,800 --> 00:21:44,300
He has a bunch of
designs like this.

487
00:21:44,300 --> 00:21:50,520
You can check out his images on
the web if you want to see more

488
00:21:50,520 --> 00:21:53,400
and diagrams.

489
00:21:53,400 --> 00:21:55,570
And I think this is our
last tessellation example.

490
00:21:55,570 --> 00:21:58,570
So here, goal is
to make US flag.

491
00:21:58,570 --> 00:22:00,250
And there's a video
of this being made,

492
00:22:00,250 --> 00:22:02,495
but it's just fold along
the lines and then collapse.

493
00:22:02,495 --> 00:22:05,062

494
00:22:05,062 --> 00:22:06,520
You're using a
tessellation element

495
00:22:06,520 --> 00:22:09,082
to get the stars in the flag.

496
00:22:09,082 --> 00:22:11,040
And this is what the
crease pattern looks like.

497
00:22:11,040 --> 00:22:12,415
So you've got a
nice tessellation

498
00:22:12,415 --> 00:22:15,350
here and then sort of a
simpler tessellation out here,

499
00:22:15,350 --> 00:22:16,980
which is just some pleats.

500
00:22:16,980 --> 00:22:20,390
And getting those pleats
to resolve to the outside.

501
00:22:20,390 --> 00:22:22,180
This is by Robert Lang.

502
00:22:22,180 --> 00:22:22,680
Very cool.

503
00:22:22,680 --> 00:22:25,910

504
00:22:25,910 --> 00:22:31,310
So next, I want to transition
to kind of modular origami

505
00:22:31,310 --> 00:22:32,930
where you use multiple parts.

506
00:22:32,930 --> 00:22:37,750
But before we get there, this
is I guess the oldest recorded

507
00:22:37,750 --> 00:22:41,590
example of a picture of origami.

508
00:22:41,590 --> 00:22:44,440
So this is from 1734.

509
00:22:44,440 --> 00:22:46,050
This is a reference.

510
00:22:46,050 --> 00:22:50,440
This is the actual object-- I
believe, a newspaper article.

511
00:22:50,440 --> 00:22:52,300
And it's a little
rough to see here,

512
00:22:52,300 --> 00:22:54,920
but there's an origami
crane and a bunch

513
00:22:54,920 --> 00:22:59,000
of other classic origami
things like water bomb.

514
00:22:59,000 --> 00:23:02,260
So the assumption is by
1734, origami was well-known.

515
00:23:02,260 --> 00:23:04,322
All the classic
models were out there.

516
00:23:04,322 --> 00:23:05,780
We don't know how
far back it goes.

517
00:23:05,780 --> 00:23:07,196
It could be as
early as when paper

518
00:23:07,196 --> 00:23:09,770
was invented which
was like 50 AD.

519
00:23:09,770 --> 00:23:14,280
Somewhere between 50 and 1734,
origami really hit it big.

520
00:23:14,280 --> 00:23:16,110
That's the big range.

521
00:23:16,110 --> 00:23:18,230
But I wanted to show this
because of the cranes.

522
00:23:18,230 --> 00:23:22,350
And one way to combine
multiple parts together

523
00:23:22,350 --> 00:23:25,140
is to combine multiple
cranes together.

524
00:23:25,140 --> 00:23:31,280
And there's this whole
world, hiden senbazuru,

525
00:23:31,280 --> 00:23:33,350
which is connected cranes.

526
00:23:33,350 --> 00:23:37,770
And orikata means you're
cutting in addition to folding.

527
00:23:37,770 --> 00:23:39,880
So this is a rectangle of paper.

528
00:23:39,880 --> 00:23:42,530
It's been split along
two lines and then folded

529
00:23:42,530 --> 00:23:44,850
into three cranes.

530
00:23:44,850 --> 00:23:47,680
So that's pretty cool.

531
00:23:47,680 --> 00:23:50,740
And there's much
more intricate ones

532
00:23:50,740 --> 00:23:53,590
where you take a square of
paper or a rectangle paper,

533
00:23:53,590 --> 00:23:57,090
do lots of cuts, subdivide your
thing into a bunch of squares.

534
00:23:57,090 --> 00:23:59,100
Each square gets
folded into a crane.

535
00:23:59,100 --> 00:24:02,939
The tips of the cranes stay
connected at these tabs.

536
00:24:02,939 --> 00:24:04,730
And the challenge when
you're folding these

537
00:24:04,730 --> 00:24:06,510
is to not tear at the tabs.

538
00:24:06,510 --> 00:24:08,720
But then you'll get
these really cool folds.

539
00:24:08,720 --> 00:24:11,310
This is an old book from
1797, not much later

540
00:24:11,310 --> 00:24:12,779
than that last reference.

541
00:24:12,779 --> 00:24:14,320
We have a copy of
this book if you're

542
00:24:14,320 --> 00:24:15,730
interested in checking it out.

543
00:24:15,730 --> 00:24:18,070
Lots of different designs.

544
00:24:18,070 --> 00:24:22,280
There have been some recent
works in making really nice.

545
00:24:22,280 --> 00:24:25,690
These are spheres out
of connected cranes

546
00:24:25,690 --> 00:24:26,810
by Linda Tomoko.

547
00:24:26,810 --> 00:24:29,600

548
00:24:29,600 --> 00:24:32,950
And here's one out
of silver foil.

549
00:24:32,950 --> 00:24:38,897
So really cool connected cranes.

550
00:24:38,897 --> 00:24:40,480
So that's a traditional
origami style.

551
00:24:40,480 --> 00:24:42,720
I want to transition
to modular origami

552
00:24:42,720 --> 00:24:45,270
where you combine lots
of identical parts,

553
00:24:45,270 --> 00:24:47,600
but now they're
actually disconnected.

554
00:24:47,600 --> 00:24:52,250
And this is a very simple unit.

555
00:24:52,250 --> 00:24:53,830
I think it's just
water bomb based.

556
00:24:53,830 --> 00:24:55,510
And then they nest
into each other.

557
00:24:55,510 --> 00:25:00,730
You've probably seen these
kind of swans, modular swans.

558
00:25:00,730 --> 00:25:02,670
I think they're a
very old tradition.

559
00:25:02,670 --> 00:25:03,570
Possibly China?

560
00:25:03,570 --> 00:25:06,570
I'm not sure exactly.

561
00:25:06,570 --> 00:25:08,160
So a kind of traditional model.

562
00:25:08,160 --> 00:25:11,530
But you get a lot of
geometric models like this.

563
00:25:11,530 --> 00:25:13,750
So these are examples
of different units.

564
00:25:13,750 --> 00:25:15,830
You take typically
a square of paper.

565
00:25:15,830 --> 00:25:20,320
You do maybe 10 or 20
folds and you get a unit.

566
00:25:20,320 --> 00:25:22,710
And then you combine a bunch
of these units together.

567
00:25:22,710 --> 00:25:25,660
So one of the classic units
is called a Sonobe unit.

568
00:25:25,660 --> 00:25:27,410
Sonobe units use
sort of backwards,

569
00:25:27,410 --> 00:25:31,540
but you can get these
kinds of cool polyhedra.

570
00:25:31,540 --> 00:25:37,100
Robert Neale, he's a magician
and an origami designer.

571
00:25:37,100 --> 00:25:37,866
Has some units.

572
00:25:37,866 --> 00:25:39,490
This one's called
the penultimate unit.

573
00:25:39,490 --> 00:25:43,750
And so you can see each of
these green strips is one unit--

574
00:25:43,750 --> 00:25:45,160
blue strip, pink strip.

575
00:25:45,160 --> 00:25:46,760
There's a lot of units in here.

576
00:25:46,760 --> 00:25:48,220
90 in total.

577
00:25:48,220 --> 00:25:50,860
Typically, one per edge of
the polyhedron, sometimes

578
00:25:50,860 --> 00:25:52,720
two per edge.

579
00:25:52,720 --> 00:25:55,270
And they lock together
in certain ways

580
00:25:55,270 --> 00:25:59,030
to really hold these
nice shapes here.

581
00:25:59,030 --> 00:26:01,850
Tom Hull folds a lot
of modular origami.

582
00:26:01,850 --> 00:26:06,050
And one of his units
is called a PHiZZ unit.

583
00:26:06,050 --> 00:26:08,110
I think it can make
anything as long as you

584
00:26:08,110 --> 00:26:11,300
have three units coming
together at each vertex.

585
00:26:11,300 --> 00:26:13,440
So as long as every
vertex has degree three,

586
00:26:13,440 --> 00:26:15,160
you can kind of make
your polyhedron.

587
00:26:15,160 --> 00:26:17,326
I guess the lengths also
have to be the same or else

588
00:26:17,326 --> 00:26:19,351
you have to adjust the
units to be different.

589
00:26:19,351 --> 00:26:20,975
So each of the units
here is identical,

590
00:26:20,975 --> 00:26:22,470
except different color patterns.

591
00:26:22,470 --> 00:26:25,870

592
00:26:25,870 --> 00:26:28,450
Here's a big example of a
PHiZZ unit construction.

593
00:26:28,450 --> 00:26:30,810
So this is 270 units.

594
00:26:30,810 --> 00:26:34,770
Take a long time to fold
probably and even more time

595
00:26:34,770 --> 00:26:37,164
to weave them together.

596
00:26:37,164 --> 00:26:39,205
Usually putting the last
piece in is the hardest.

597
00:26:39,205 --> 00:26:42,190

598
00:26:42,190 --> 00:26:44,080
Here's some more
examples by Tom Hull.

599
00:26:44,080 --> 00:26:47,200
He has another unit
called the hybrid unit.

600
00:26:47,200 --> 00:26:50,860
And this is what three of
them look like woven together.

601
00:26:50,860 --> 00:26:54,800
So this paper is probably red
on one side, black on the other.

602
00:26:54,800 --> 00:26:57,900
And there's one unit that
comes here, wraps around

603
00:26:57,900 --> 00:27:00,599
the tetrahedron, and two more.

604
00:27:00,599 --> 00:27:02,140
And you combine them
and you can make

605
00:27:02,140 --> 00:27:05,000
all these different
regular solids.

606
00:27:05,000 --> 00:27:08,800
And you get these
spiky tetrahedra

607
00:27:08,800 --> 00:27:10,890
on each of the faces
which is pretty cool.

608
00:27:10,890 --> 00:27:13,200
So this like icosahedra,
a regular 20-sided

609
00:27:13,200 --> 00:27:15,610
die, on the inside here,
but then each of them

610
00:27:15,610 --> 00:27:18,750
has a spike from there.

611
00:27:18,750 --> 00:27:20,710
And here's a big one he made.

612
00:27:20,710 --> 00:27:22,690
This is actually one of
my favorite polyhedra,

613
00:27:22,690 --> 00:27:24,956
the rhombicosidodecahedron.

614
00:27:24,956 --> 00:27:30,425
It's got all the polygons--
squares, triangles, hexagons,

615
00:27:30,425 --> 00:27:33,390
if I recall correctly.

616
00:27:33,390 --> 00:27:35,221
It's obvious, right?

617
00:27:35,221 --> 00:27:37,720
And one of the challenges here
is getting the color patterns

618
00:27:37,720 --> 00:27:40,730
to be nice and
symmetric and even.

619
00:27:40,730 --> 00:27:43,710
And Tom Hull is one of
the experts in that.

620
00:27:43,710 --> 00:27:46,989
He's a mathematician,
but also an origamist.

621
00:27:46,989 --> 00:27:48,530
And then he started
combining the two

622
00:27:48,530 --> 00:27:49,830
because of problems like this.

623
00:27:49,830 --> 00:27:53,650

624
00:27:53,650 --> 00:27:55,650
Next we get to polypolyhedra.

625
00:27:55,650 --> 00:27:58,320
This is the idea of
taking multiple polyhedra

626
00:27:58,320 --> 00:28:00,360
and weaving them
together and then making

627
00:28:00,360 --> 00:28:01,800
that out of origami.

628
00:28:01,800 --> 00:28:03,950
And this is one of the
most famous designs

629
00:28:03,950 --> 00:28:07,280
in this family called FIT, or
Five Intersecting Tetrahedra,

630
00:28:07,280 --> 00:28:08,470
designed by Tom Hull.

631
00:28:08,470 --> 00:28:12,030
This is a photograph of one
that I am the proud owner.

632
00:28:12,030 --> 00:28:15,410
It was folded by
Vanessa Gould, who

633
00:28:15,410 --> 00:28:18,250
directed Between the Folds,
which is the documentary you

634
00:28:18,250 --> 00:28:21,440
all heard about when
Jason mentioned it.

635
00:28:21,440 --> 00:28:23,850
And it's available free
streaming on Netflix,

636
00:28:23,850 --> 00:28:26,280
so you should all watch it.

637
00:28:26,280 --> 00:28:27,820
Or we could have a showing here.

638
00:28:27,820 --> 00:28:29,690
Actually, how many
people are interested?

639
00:28:29,690 --> 00:28:32,910
Haven't seen the movie or
would like to see it again

640
00:28:32,910 --> 00:28:35,361
related to this
class some evening?

641
00:28:35,361 --> 00:28:35,860
OK.

642
00:28:35,860 --> 00:28:39,030
That's maybe enough
to do a showing.

643
00:28:39,030 --> 00:28:40,530
Anyway, she folded this.

644
00:28:40,530 --> 00:28:44,360

645
00:28:44,360 --> 00:28:45,240
Cool.

646
00:28:45,240 --> 00:28:50,440
And then Robert Lang enumerated
all possible polypolyhedra

647
00:28:50,440 --> 00:28:52,447
that are symmetric
in a certain sense.

648
00:28:52,447 --> 00:28:54,780
And these are two examples
that he thought were so cool.

649
00:28:54,780 --> 00:28:56,110
He made them out of paper.

650
00:28:56,110 --> 00:28:58,600
Most of them just exist
as virtual designs.

651
00:28:58,600 --> 00:29:01,130
People have been folding
them, but there's

652
00:29:01,130 --> 00:29:03,154
hundreds if not
thousands in his list.

653
00:29:03,154 --> 00:29:04,570
So if you're
interested, check out

654
00:29:04,570 --> 00:29:06,110
his website on polypolyhedra.

655
00:29:06,110 --> 00:29:09,010

656
00:29:09,010 --> 00:29:11,070
These are, again, modular.

657
00:29:11,070 --> 00:29:14,010
And finally, we come
to modules of cubes.

658
00:29:14,010 --> 00:29:16,180
And this is why you
have business cards.

659
00:29:16,180 --> 00:29:18,980
And I thought we
could play with this.

660
00:29:18,980 --> 00:29:23,540
This is a life-size chair made
from a particular unit, which

661
00:29:23,540 --> 00:29:26,680
is out of business cards,
folding these individual cubes

662
00:29:26,680 --> 00:29:29,260
and then sticking them
together in a particular way.

663
00:29:29,260 --> 00:29:31,500
Unfortunately, the
material's not strong enough

664
00:29:31,500 --> 00:29:33,200
to actually support much weight.

665
00:29:33,200 --> 00:29:35,920
So you can't sit on this
chair, but it looks just

666
00:29:35,920 --> 00:29:36,830
like a real chair.

667
00:29:36,830 --> 00:29:38,710
It's very cool.

668
00:29:38,710 --> 00:29:41,870
You can make any set of cues
you like and interlock them

669
00:29:41,870 --> 00:29:43,310
together.

670
00:29:43,310 --> 00:29:47,500
One of the craziest
experimenters with this cube

671
00:29:47,500 --> 00:29:49,980
module is Jeannine
Mosely, who's a MIT

672
00:29:49,980 --> 00:29:52,310
alum and lives in the area.

673
00:29:52,310 --> 00:29:56,430
And she became really famous for
making this Menger Sponge out

674
00:29:56,430 --> 00:29:58,190
of 66,000 business cards.

675
00:29:58,190 --> 00:30:01,580
It took something like
five years to make this.

676
00:30:01,580 --> 00:30:04,270
She made a lot of
the units herself.

677
00:30:04,270 --> 00:30:07,830
And so this is trying to
represent a particular fractal,

678
00:30:07,830 --> 00:30:08,820
which is pretty cool.

679
00:30:08,820 --> 00:30:11,750
You start by taking a cube
and then drilling holes

680
00:30:11,750 --> 00:30:15,270
through each of the sides
in the center third.

681
00:30:15,270 --> 00:30:16,410
So this is one iteration.

682
00:30:16,410 --> 00:30:18,455
You just drill
through that hole,

683
00:30:18,455 --> 00:30:20,940
that hole, same on each side.

684
00:30:20,940 --> 00:30:22,730
Remove that material.

685
00:30:22,730 --> 00:30:25,960
That leaves you
with-- how many cubes?

686
00:30:25,960 --> 00:30:27,150
Eight cubes on top.

687
00:30:27,150 --> 00:30:28,233
Eight cubes on the bottom.

688
00:30:28,233 --> 00:30:32,790
Four cubes in the
middle, which is 20.

689
00:30:32,790 --> 00:30:34,784
For each of the 20
cubes, you recurse.

690
00:30:34,784 --> 00:30:36,200
So for each of
those 20 cubes, you

691
00:30:36,200 --> 00:30:39,520
drill holes, drill holes
from all the sides.

692
00:30:39,520 --> 00:30:42,790
And after two iterations,
you have this structure.

693
00:30:42,790 --> 00:30:45,410
After three iterations,
you have this structure.

694
00:30:45,410 --> 00:30:47,699
After infinitely
many iterations--

695
00:30:47,699 --> 00:30:48,990
well, no, this is not infinite.

696
00:30:48,990 --> 00:30:53,520
But this is actually the same
number of iterations as that.

697
00:30:53,520 --> 00:30:54,870
So in principle, you keep going.

698
00:30:54,870 --> 00:30:58,680
But at any fixed point, you can
treat the smallest little unit

699
00:30:58,680 --> 00:31:01,110
that hasn't been recursed
as one of these cubes,

700
00:31:01,110 --> 00:31:03,310
build that, and then
assemble them together.

701
00:31:03,310 --> 00:31:04,590
It's challenging.

702
00:31:04,590 --> 00:31:06,751
You could not take this--
with the business cards,

703
00:31:06,751 --> 00:31:08,250
you could not go
to the next level--

704
00:31:08,250 --> 00:31:09,666
not because it
would take forever,

705
00:31:09,666 --> 00:31:12,130
but also because it would
collapse under its own weight.

706
00:31:12,130 --> 00:31:14,270
So trade-off there.

707
00:31:14,270 --> 00:31:16,440
That was 66,000 business
cards, five years.

708
00:31:16,440 --> 00:31:19,100
I thought, man, that
was a big project.

709
00:31:19,100 --> 00:31:22,380
But then Jeannine says,
what else can we make?

710
00:31:22,380 --> 00:31:25,410
And she got more volunteers
for these future projects

711
00:31:25,410 --> 00:31:27,210
so they were made a lot faster.

712
00:31:27,210 --> 00:31:28,540
This is a cool fractal.

713
00:31:28,540 --> 00:31:34,290
Not quite as many,
50,000 business cards.

714
00:31:34,290 --> 00:31:36,399
And this is a fractal
that she designed.

715
00:31:36,399 --> 00:31:37,315
Kind of complimentary.

716
00:31:37,315 --> 00:31:41,830
You take a cube and subdivide
it into three by three by three,

717
00:31:41,830 --> 00:31:45,210
and then remove all the corner
cubes, and then recurse.

718
00:31:45,210 --> 00:31:46,970
And she calls it the
Moseley Snowflake

719
00:31:46,970 --> 00:31:49,700
because if you look
at it from the corner,

720
00:31:49,700 --> 00:31:54,000
you get this nice Koch
snowflake outline.

721
00:31:54,000 --> 00:31:57,056
And this is the real
one from the same view.

722
00:31:57,056 --> 00:32:00,660
It's a little big, so it's
hard to see it all in one shot.

723
00:32:00,660 --> 00:32:03,510
And so that's pretty awesome.

724
00:32:03,510 --> 00:32:06,800
And then her most recent project
was 100,000 business cards.

725
00:32:06,800 --> 00:32:09,130
This is I guess the
world record for origami

726
00:32:09,130 --> 00:32:11,220
made from business cards.

727
00:32:11,220 --> 00:32:13,140
And this is a model
of Union Station

728
00:32:13,140 --> 00:32:17,372
in Worcester, Massachusetts.

729
00:32:17,372 --> 00:32:19,080
Hundreds of volunteers
here to make this.

730
00:32:19,080 --> 00:32:23,640
This was done for first night
celebration a year or so ago.

731
00:32:23,640 --> 00:32:25,130
Pretty amazing.

732
00:32:25,130 --> 00:32:28,160
And you can see, you can really
sculpt with these cube units,

733
00:32:28,160 --> 00:32:29,090
do lots of cool stuff.

734
00:32:29,090 --> 00:32:34,930
And there's a few extra
details on the surface there.

735
00:32:34,930 --> 00:32:37,772
So I thought we
would make something.

736
00:32:37,772 --> 00:32:39,790
So these are diagrams
you can start working

737
00:32:39,790 --> 00:32:43,190
or I can tell you
about how they work.

738
00:32:43,190 --> 00:32:47,240
Each cube is made from six
identical business cards.

739
00:32:47,240 --> 00:32:49,340
I have here my
own business cards

740
00:32:49,340 --> 00:32:53,280
from when I first
arrived, old classic.

741
00:32:53,280 --> 00:32:55,900
So you start by taking two
of your business cards.

742
00:32:55,900 --> 00:32:58,610
You have to decide whether
you want the white face up

743
00:32:58,610 --> 00:33:00,540
on your cube and make
it nice and clean

744
00:33:00,540 --> 00:33:04,120
or you want the pattern side up.

745
00:33:04,120 --> 00:33:05,740
Whichever one you
want to expose,

746
00:33:05,740 --> 00:33:08,570
you keep that on the outside
and you bring the two cards

747
00:33:08,570 --> 00:33:09,410
together.

748
00:33:09,410 --> 00:33:13,420
So in this case, I'm going
to make the pattern side out.

749
00:33:13,420 --> 00:33:16,230
And you want to align
these approximately evenly.

750
00:33:16,230 --> 00:33:20,420
You want them as perpendicular
as possible and then

751
00:33:20,420 --> 00:33:22,780
roughly evenly spaced.

752
00:33:22,780 --> 00:33:27,190
And then you just
mountain fold both sides.

753
00:33:27,190 --> 00:33:31,855
So you want mountain folds on
the side that you care about.

754
00:33:31,855 --> 00:33:33,230
And that gives
you a nice square.

755
00:33:33,230 --> 00:33:36,870
Now I've got two nice
squares folded like this.

756
00:33:36,870 --> 00:33:39,605
Repeat three times,
you get six units.

757
00:33:39,605 --> 00:33:56,080

758
00:33:56,080 --> 00:34:12,520
Four and six.

759
00:34:12,520 --> 00:34:14,760
OK, once you've
got the six units,

760
00:34:14,760 --> 00:34:16,510
you want to combine
them together.

761
00:34:16,510 --> 00:34:18,409
This is where it gets fun.

762
00:34:18,409 --> 00:34:21,409
And it's helpful to look
at this diagram down here.

763
00:34:21,409 --> 00:34:23,254
These are some diagrams
by Ned Batchelder.

764
00:34:23,254 --> 00:34:26,650

765
00:34:26,650 --> 00:34:29,710
And so this idea of making
cubes has been around.

766
00:34:29,710 --> 00:34:33,020
I think it was Jeannine's
idea to combine them together.

767
00:34:33,020 --> 00:34:35,730
So this is what one
cube looks like.

768
00:34:35,730 --> 00:34:38,130
Why don't I fold,
make one of them.

769
00:34:38,130 --> 00:34:40,969
Basically, you want the
tabs going on the outside.

770
00:34:40,969 --> 00:34:44,270
And you need to alternate
so they lock together.

771
00:34:44,270 --> 00:34:46,350
And you need to alternate
between oriented

772
00:34:46,350 --> 00:34:49,219
horizontal and
oriented vertical.

773
00:34:49,219 --> 00:34:54,350
So they recommend starting by
making a corner, three of them

774
00:34:54,350 --> 00:34:58,935
like that, and then
fill around the outside.

775
00:34:58,935 --> 00:35:08,090

776
00:35:08,090 --> 00:35:11,710
And then as usual, putting in
the last piece is the hardest.

777
00:35:11,710 --> 00:35:14,350
So I've got to get--
I want all the tabs

778
00:35:14,350 --> 00:35:16,710
on the outside like that.

779
00:35:16,710 --> 00:35:21,120

780
00:35:21,120 --> 00:35:23,060
And I probably
should've mentioned--

781
00:35:23,060 --> 00:35:26,000
fold the creases really hard.

782
00:35:26,000 --> 00:35:28,860
You can do that to a certain
extent afterwards, make it nice

783
00:35:28,860 --> 00:35:31,260
and cubey.

784
00:35:31,260 --> 00:35:35,090
But in this case, I got
my six-sided cube out

785
00:35:35,090 --> 00:35:35,920
of those six units.

786
00:35:35,920 --> 00:35:38,840
It's got my name
right in the center.

787
00:35:38,840 --> 00:35:42,360
So you can design business card
specifically for this purpose.

788
00:35:42,360 --> 00:35:43,670
I accidentally did.

789
00:35:43,670 --> 00:35:45,960
And that's how
you make one cube.

790
00:35:45,960 --> 00:35:49,600
Once you've got two cubes,
you can lock them together

791
00:35:49,600 --> 00:35:53,180
by just twisting them 90
degrees relative to each other

792
00:35:53,180 --> 00:35:56,810
and just sliding the tabs
in, just sliding the tabs in.

793
00:35:56,810 --> 00:35:59,620
This is also like
doing that last move.

794
00:35:59,620 --> 00:36:02,275
So this tab's got to go in
here between these two tabs.

795
00:36:02,275 --> 00:36:06,012

796
00:36:06,012 --> 00:36:07,470
It wouldn't hold
together very well

797
00:36:07,470 --> 00:36:10,140
if it wasn't hard
to put together.

798
00:36:10,140 --> 00:36:13,260
So once you've got them
together, you've got two cubes.

799
00:36:13,260 --> 00:36:15,240
Now if you want, for
a finishing touch,

800
00:36:15,240 --> 00:36:23,070
you can also make another
unit and cover the surfaces.

801
00:36:23,070 --> 00:36:24,960
So all of Jeannine
Moseley's examples

802
00:36:24,960 --> 00:36:31,150
are done this way where at
the end-- I haven't tried this

803
00:36:31,150 --> 00:36:34,995
lately-- you stick on a business
card just on the surface

804
00:36:34,995 --> 00:36:38,600
so it interlocks here and
then interlocks over here.

805
00:36:38,600 --> 00:36:42,070
Ho boy, this is challenging.

806
00:36:42,070 --> 00:36:46,196
And then you get a full square
business card on the outside.

807
00:36:46,196 --> 00:36:48,820
And you can use this to, if you
have different colored business

808
00:36:48,820 --> 00:36:52,100
cards or you want a nice,
clean white surface, no seams.

809
00:36:52,100 --> 00:36:53,540
So you have these
tabs right now,

810
00:36:53,540 --> 00:36:55,081
but once you add
something like this,

811
00:36:55,081 --> 00:36:57,730
you have a nice seamless
square on the outside.

812
00:36:57,730 --> 00:37:00,530
So you use up more
business cards,

813
00:37:00,530 --> 00:37:04,090
but it can make for
a nicer surface.

814
00:37:04,090 --> 00:37:06,930
So any questions
about making these?

815
00:37:06,930 --> 00:37:09,590
I thought we would make some
and then build something.

816
00:37:09,590 --> 00:37:12,870
But for that, I need
suggestions on what to build.

817
00:37:12,870 --> 00:37:14,156
Oh, an MIT.

818
00:37:14,156 --> 00:37:15,008
I like that.

819
00:37:15,008 --> 00:37:16,140
Let's make an MIT.

820
00:37:16,140 --> 00:37:17,160
So let's design.

821
00:37:17,160 --> 00:37:22,070
So by MIT, do you mean
MIT logo or like an M?

822
00:37:22,070 --> 00:37:25,460
1, 2, 3, 4, 5, 6,
7, 8, 9, 10 cubes.

823
00:37:25,460 --> 00:37:25,960
Easy.

824
00:37:25,960 --> 00:37:29,660

825
00:37:29,660 --> 00:37:33,240
Exploding cubes.

826
00:37:33,240 --> 00:37:37,891
I wonder if you can use
these to make pinatas?

827
00:37:37,891 --> 00:37:38,390
MIT.

828
00:37:38,390 --> 00:37:42,790

829
00:37:42,790 --> 00:37:44,960
We could also just make
a row at the bottom.

830
00:37:44,960 --> 00:37:48,440
One cube higher.

831
00:37:48,440 --> 00:37:50,919
Four more minutes.

832
00:37:50,919 --> 00:37:52,851
AUDIENCE: We could
do Minecraft origami.

833
00:37:52,851 --> 00:37:54,300
AUDIENCE: Ohh.

834
00:37:54,300 --> 00:37:55,132
AUDIENCE: Oh, yes!

835
00:37:55,132 --> 00:37:56,340
AUDIENCE: That's a good idea.

836
00:37:56,340 --> 00:37:59,080
PROFESSOR: Minecraft
is a good source.

837
00:37:59,080 --> 00:38:29,107