Print PDF
Favorite
Email
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.
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.
Remove these ads by
Signing UpStep 1Make 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.
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.
| « Previous Step | Download PDFView All Steps | Next Step » |
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.
You can't create a non-3D object in a 3D universe.
(perhaps with the exception of a Nobius strip)
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?
What is two-space? You're losing me here.
The same applies for projection.
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.
one is enclosed, which is basically a large cube with a smaller cube inside, with its corresponding vertexes joined together with lines (in this version, like the next, has 8 'rooms', one in the center, 6 represented by the warped cubes along the sides, the top and bottom, and the 8th one being the surrounding space around this figure, which is easier to understand in the second figure).
the other figure is inside-out (or unfolded), and looks like four cubes stacked on top of each other, with four more cubes connected along the sides of the second to the bottom cube on the stack (depending on how you unfold it). it looks like an upside down 3D crucifix (this figure also has 8 'rooms', but they're more ... corporeal ...in this shape.... the 'outside' room is now the room in the middle of the 4 protruding cubes, the 'center' cube from before is now the very top cube, the 'top' cube should now be at the bottom of the figure, and the 'bottom' cube should now be second from the top, right under the 'center' room. the 4 rooms around the sides of the enclosed figure should now be the ones protruding outward.)
this figure you've made does demonstrate all 8 rooms, but it's a bit more confusing visually.
the purpose of the 4th dimension of this shape is that it allows you to move from one 'room' to the other in a straight line and come back to where you started. it doesn't really have anything to do with time travel in the commonly used sense, but simply uses the 4th dimension as a way to fold across the 3rd to come back to where you started. unfortunately, since all walls are connected to the walls of the other cubes, once inside such a structure it would be impossible to exit. every exit in this 'crooked house' would lead to one of the other 7 rooms. an awesome short story by Robert A. Heinlein called "And He Built a Crooked House " explains how being inside this theoretical structure would work, though takes an artistic license with how they get out of it. you can read it here: http://www.scifi.com/scifiction/classics/classics_archive/heinlein/heinlein1.html
hope that helps anyone who doesn't understand what they're making with Popsicle sticks. :P
BUT, a tesseract has a different kind of dimension (another dimension of space, but it still has 4 dimensions). The 4th dimension of the tesseract is the "W-axis"... the directions are: left, right, up, down, forward, backward, ana, upsilon, wint, kata, delta, and zant.
Goto:
http://en.wikipedia.org/wiki/Fourth_dimension
of the path in that case are equivalent to counting in the binary
GRAY CODE, which has been used by computer mouses and also
"encoders" which are generally used as digital volume controls.
The path goes from point to point of all the corners by way of
the edges of the n-dimensional cube without intersecting.
Considering a 3D "unit cube" (of width = 1) the path is
XYZ:
000
001
011
010
110
111
101
100
(000)-return to point of origin
This makes a graph resembling two staples or wickets whose
end points are connected by 2 parallel lines and only 8 of the 12
cube edges are needed to complete the path connecting all
the corners. No faces are crossed.
Converting binary from and to gray code for any purpose including
visiting all the vertexes of a hyperdimensional cube is done
simply with exclusive-or logic. Gray code might not be useful
for arithmetic but for the purpose of registering positions it is
efficient because counting in it always changes only one bit.
For more info, google "gray code", or "mathworld gray code".
"Exclusive-or logic" may also seem bizarre, with uncanny usefulness.