## Four-Dimensional Rubik's Cube Craziness 296 296

roice writes

*"Rubik's junkies and puzzlers will be interested in this software rendered four-dimensional analog of Rubik's Cube. With over 1.75E120 possible combinations, it's a mind bender. Free versions are available for both Windows and Linux, and they even publish their source code for download. Solving it will get your name listed in their Hall Of Fame, and there is also a running competition for the most efficient solution. To help get you started, you can check out a solution algorithm based on techniques used to solve the popular three-dimensional version."*
## damn it.... (Score:5, Interesting)

## Tried it a while back. (Score:2, Interesting)

## Anyone remember "Cubey"? (Score:4, Interesting)

The 1980s certainly seemed the nadir of American animation...

## Is this actualy 4D ? (Score:5, Interesting)

Maybe it's because I read some quack's claim that the 4th dimension was time. In which case a 4D rubics cube would solve itself over time or be onsolvable because it rescrambled while you were trying to solve.

## Re:nooo (Score:5, Interesting)

Jason

ProfQuotes [profquotes.com]

## Re:Is this actualy 4D ? (Score:5, Interesting)

http://dogfeathers.com/java/hyprcube.html

It's really tough to wrap your head around another spatial dimension. Books like Flatland and Realware make the comparison to a 2D person's world being interrupted by one of us.

For example, if you were 2D, living on your flat plane, and a 3D person passed an orange through the plane, you would perceive it as a round shape which grew out of nothingness, got bigger and changed shape for awhile, then shrank and disappeared.

A 3D person could also see into your house, because a 2D person would just build four walls and no ceiling or floor. Similarly, a 4D creature could see through all of us and our buildings, because we only build in three dimensions.

## Re:Is this actualy 4D ? (Score:2, Interesting)

0. Start with a point. Zero dimensions. (Draw a dot.)

1. Expand each vertex in a direction you haven't used yet. (Draw a horizontal line from the dot, and put a dot at the end of it.)

Now you have a line, one dimension.

2. Expand each vertex in a direction you haven't yet, and connect them. (Draw vertical line from each dot, and a horizontal line connecting the two new dots.)

Now you have a square, two dimensions.

3. Expand each vertex in a direction you haven't yet, and connect them. Since we have run out of actual dimensions on our sheet of paper, we will have to create virtual dimentions. Sorry if I've offended a topologist, I don't know the technical terms. (Draw one diagonal line from each of the four dots of the square, to the top and right. Connect the four new dots with another square. Most of you are probably familiar with this 2D projection of a 3D cube.)

Now you have a cube, three dimensions.

4. Expand each vertex in a direction you haven't yet, and connect them. We have to create more virtual dimensions, so this might seem a little tricky. (Imagine a cube in 3D-space, and imagine what it would look like with lines protruding from the center of the cube, through each corner. Draw these eight lines, then connect their endpoints, one square on top of the cube, one square on the bottom, then four vertical lines connecting each of the two new squares.)

If you did it correctly, you should end up with what looks like a cube, encased within a larger cube, with lines from the corners of the inner cube to the corresponding corners of the outer cube.

## 4D analogs for mathematics behind Rubik's cube? (Score:2, Interesting)

Using this group, you could do various things like find the odds that a random arrangement of stickers is actually solvable (take the size of the group divided by the number of possible arrangements). Are there computations involving this for the 4D cube on the web anywhere?

## Re:Is this actualy 4D ? (Score:3, Interesting)

Example, take a room, it has 3 standard dimensions, now lets add another dimension, lets say temperature. Now we have a 4d object, we could even try and make a function to model temperature based on postion, temp = f(x,y,z);

You can even do neat things like make 3d objects out of 4d objects by taking a level surface of the 4d object. In simpler terms, take all of the points in the room that are one temperature, that will form a 3d object.

I think the easiest way to portray a 4d object is by using colour. Image taking a pair of thermal gogles and walking around a room. The only problem is that a colour approach cant be used for rubix cubes, becuase colour is already used to distinguish different sides of the cube. Perhaps to visualize a 4d rubix cube the different sides of the cube could be represented by shapes, or perhaps a numbering system. I think that taking the 4d cube and trying to flatten it into 3d looks ugly.

## Oh my eyes! (Score:2, Interesting)

Blue links and black test on a dark grey background. What was this guy thinking?