Four Dimensional Rubik's Cube

[JohnGay]

Here is a paper replica of a four dimensional Rubik's cube (-=



And solved!


Very interesting getting it to twist in the fourth dimension (-=

Puzzling.

[airdave]

What do you mean "four" dimensional?
It moves in time?


...
It looks like a puzzle with more than 6 sides (standard cube).
For example, a dodecahedron has 12 sides.
IS that what you are talking about...extra sides?

[JohnGay]

Here is a cross-eyed projection of a four dimensional cube viewed corner-on.


Although it appears transparent, actually you are only seeing the front 4 cubic faces.
There are another 4 cubic faces hidden behind these faces in the fourth dimension.
And the cubes are distorted into rhombic shapes due to being projected into 3 dimensions.

Cheers,

John Gay

[Kevin WS]

I don't get it all!

[gotham]

I don't care how many dimensions it has, I've never been able to solve of Rubik Cube.

[airdave]

The fourth dimension of measurement is time.
The fourth dimension of television is The Twilight Zone.

You are using Dimension 4 to represent the unseeable or hidden faces?
Your "cube" is from the Twilight Zone?

A "cube" is a three dimensional object by human design with only 6 sides.

What you've designed is not a cube and yet, is still a 3-Dimensional object.
No matter how many faces or if any of them are transparent.

Or, are you suggesting the unseen sides only exist in an alternate or parallel reality?
If so, isn't your doppelganger solving that cube?
And...is Roy Thinnes playing your doppelganger in the movie?

[fitz301]

You've managed to model a polyhedron, doesn't have anything to do with the fourth dimension - unless you've also managed to invent a time machine.

[cfuruti]

Originally Posted by fitz301

You've managed to model a polyhedron, doesn't have anything to do with the fourth dimension .

Yes, it looks like a rhombic dodecahedron.

[Kevin WS]

I'm going to have to have another think about this...

[JohnGay]

Although Einstein described time as an additional dimension to the space dimensions we were used to, mathematically, 4 dimensional and even higher dimensions were well described. Edwin Abbott Abbott used it as the basis of his novella Flatland in 1884.
And current quantum mechanical string theory postulates at least 11 and up to 26 or more dimensions to describe the current universe.

For a 4 dimensional hypercube projected to 3 dimensional space, the cubic 3D faces are distorted to a rhombus cube. The 4 nearest cubic faces create a rhombic dodecahedron in 3 dimensional space. The 4 further cubes will exist within the same space behind the front cubes.
Identical to the way a 3 dimensional cube drawn on a 2 dimensional page is distorted.
The 3 near faces appear as 3 rhombi within a hexagon hiding the 3 far faces.

So, although in our 3 dimensional space, this looks like just a rhombic dodecahedron, it represents a 4 dimensional hypercube patterned like a Rubik's cube with it's 3X3 faces.

Of course, the corner-on view of the hypercube is a very limited view, but getting the paper to rotate along the 4th dimension for other views would violate our 3 dimensional physics.