# Make a "real" Tesseract - 4D Cube.

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## Introduction: Make a "real" Tesseract - 4D Cube.

This is easy, like making a real 3D cube out of anything.
I did it for the first time using popsicle sticks.
It was hard so I don't recommend using popsicle sticks,
maybe skewers and super balls.

I call this a real tesseract because although it's stuck in 3D space,
it has all it's edges of equal length, just like a real cube or a real square.

Often tesseracts are illustrated as a small cube inside a big one.
Not this one! And No, this is not an "impossible object" illusion!

Why did I Make this?
1.A sculpture and to see how hard it was.
2.Imagining the possibilities of making (the frame of) a
"flux conductor" or a "flux inductor" ...
maybe even a "flux capacitor".
3.Wondering what would happen if I made the items in "why #2".
4.It's about time I Make something new on here!

A flux conductor or inductor would perhaps be a wire that follows a
"hamiltonian circuit path" around the hypercube.
That means a wire that goes to each corner only once,
of a square object of any amount of dimensions.

Tesla had not much more than wire to use as electronic parts.
Who knows what an electric tesseract might do?

This model was inspired by the 2D drawing of a hypercube (tesseract).
A Cube is an object with 6 sides which are squares.
A Hypercube is an object with 8 sides which are cubes.

## Step 1: Make a Cube

This should be easy, just make two squares and then add equally long
lines between them.

It's not so easy with ice cream sticks. I cut angles on the ends so they
were shaped like parallelograms (with a miter) hoping they would line
up perfectly at the corners. I did not do any math to see if 45 degrees
is the correct angle, and still now have not.

In "junkyard mode", I propped it up with cans barely successfully while
I glued it.

## Step 2: Make Another Cube... Wait!!!

The second cube is going to be harder.
It must be linked to the other cube like a chain,
so that one corner of it is inside the other cube.

It was really hard to make this second cube with
ice cream sticks and glue, because it needed to be
shimmed up, supported above the bottom of the other cube,
in a way so that it wouldn't fall apart.

Yes, I'm using the same picture again.

## Step 3: Connect the Corners of the Cubes

Lift up the second cube into a position where
you can connect the corners together with
8 more sticks. There are actually a lot of
possible positions where you can connect the
second cube. These correspond to rotating
the hypercube somewhat , in a way.

But find one place you can support the upper cube and
all the corners are one stick-length from the corners on the
other cube. Then add those sticks.

Just like you connect the same corners of two squares,
connect the same corners of two cubes to make the hypercube.

## Step 4: Done. Now Think of Weird 4 Dimensional Experiments.

Picture is not ready now. The glue is still drying.

Ideas I haven't tried yet:

1.Wire a hamiltonian circuit around the hypercube and run small currents
through it. Put a gimbaled or regular compass in the middle and see if
anything weird happens.

2.Wire the hamiltonian circuit and then hit it with a "quarter shrinker"
and see if you get a black hole or something. I don't know yet.

3.Make the hypercube out of metal and see if it rings like a triangle,
or has any other musical properties.

4.Wire up the hypercube with lines of EL-wire (neon wire) and use a
microcontroller to illuminate the 8 cubes in sequence. Actually LED's
would be easier to use. If done well, any hyperdimensional magic
(magnetic) should be detectable, but the lit-up-cubes will look like
cubes and you will be able to prove at science fair that hypercube
sides are 8 regular cubes. To do this you may have to stare at the
completed tesseract until your imagination shows you clearly where
all 8 of the regular cubes in the hypercube are , and when "illuminated"
everyone else will see them too.

5. hmmm... ? I'll see you again yesterday!

Pictures: (All of the Same Object)
First: One of the "emergent" (not made) cubes illuminated with EL wire.
Second: View with EL wire off.
Third:Typical "tesseract" looking view , a small cube appears inside.

## Step 5: What's a Flux Reactor?

especially one who is familiar with fractal antennas,
what he might expect of a "reactive" component
consisting of the tesseract made entirely of THESE:

(Picture of a primarily inductive, secondarily capacitive
reactance element made of part of my tesseract.)

Reactance is ... an imaginary resistance characteristic of
inductors and capacitors which actually affects alternating currents.

This could be just another "scalar wave generator",
which in my experience is useless, but ya never know.
It is a typical "resonating tank" or "loopstick antenna",
with a specific resonant frequency or band.

IF weird people do weird things, THEN weird things happen! - Logical?

An ordinary mouse is the preferred controller for selecting which,
if only one, of these reactive elements is driven at a time, because
it is encoded in gray code, which counts in the order of a
hamiltonian circuit, which again is the path to all the vertexes of
a hypercube of any (in this case 4) dimensions. Think outside the 4D box!

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• ### Game Design: Student Design Challenge

how to make a SOLID Tesseract?

I just had a crazy thought. If shining a light on a 3-d object causes a 2-d shadow, would that mean that the shadow of a tesseract would be 3-d?

Yes, the projection will be a 3D object, provided you use a torch from a 4D world

No, you'd be projecting it onto a 2-d surface no matter what.

no it wont be anything because we live in a 3 d world. there is no real 4th dimension(as you are reffering to it)

the small cube in a cube is used for some 2-d renderings.turn your model around a bit and if you find the correct angle to look at it thats what you will see.

lbenedetti is correct. The reason the x y and z sides of a tesseract have uneven sides is because the tesseract we are familiar with is just a 3D shadow of the real thing. If you take a wirefram cube and shine a light on it the shadow is a square with a smaller square inside of it. Pop it up a dimension, and boom, you've got a tesseract.

The only problem that I have not read on here yet is the fact that his representation of the tesseract has equal sides. As Carl Sagan states when an object moves down a dimension it loses it's regular properties meaning that it is no longer made up of right angles and equal lines. Sagan shows this perfectly by taking a
3-D glass cube and showing it's reflection on a flat (2-D) surface. If you were to take the tesseract from the 4th dimension to the 3rd it would no longer have the 90 degree angles or the equidistant sides.

A more appropriate title might be "a projected tesseract"; this is no more a tesseract than two squares joined by lines in the plane, of length equal to the sides of said squares, is a cube.

I agree mostly. But it's definitely 3-D and can be used as a model or frame for education and experiments. Since I haven't done them yet, I can't make any claims. It is reasonable to expect nothing unusual will happen.

It's definitely 3D, but you said it was real and 4D.

You can't create a non-3D object in a 3D universe.

(perhaps with the exception of a Nobius strip)

you can create a "2-d" object: a shadow is a 2 dimensional "object" in a 3-dimensional world.

Not really. Not enough coordinates means we won't be able to interact with it. Too many coordinates mean we just use the 3 standard coordinates.

With the fact that a 2 dimensional object casts a 1d shadow and a 3d object casts a 2d shadow, does that mean that a 4d object casts a 3d shadow?
If it did, I could see in the future all kinds of strange things being created as by-products of the fourth dimension, possibly even in a state of matter?

A shadow isn't an object. You see an object when light strikes it, bounces off and hits your eyes... basically. Where there is no light, since something is obstructed, it casts a shadow.

An "Object" is relative to the space in which it resides. In two-space, there is no light, since light is both a particle and a wave. Hence, a shadow can be considered an object. Also, if you don't like the shadow analogy, what about a projection?

Right, which is why my conjecture is that the number of dimensions an object has = the number of dimensions in the universe that possesses it.

What is two-space? You're losing me here.

The same applies for projection.

1-space = 1d 2-space = 2d 3 space = 3d etc. those terms are used in vector math, generally, when you expand theorems in the second dimension into the third, fourth, etc.

Since a shadow does not reflect light, it is most definitely not 3 dimensional. However, it IS an object. An example of an object that doesn't reflect light is glassware in a glass of oil. The Object DOES NOT reflect light; the light passes right through it.

Just because you can't see something doesn't mean that it isn't an object. IE Air, light doesn't bounce off of it much, but it's still an object.