...it requires .NET. Thanks. I don't mind downloading and installing 30MB's of framework just to play with a Rubik's cube. Really, I don't.

Given that i probably will be dead within the next 100 years i doubt i'll have time to finish it anyways, it's just to many dimensions..

You should read Diaspora [wikipedia.org] by Greg Egan.

And the least time in which I could solve the cube was 20 minutes.

Using a few simple, easy-to-learn algorithms, and with a few weeks practice it is possible for pretty much anyone to solve the 3D cube in just 2 or 3 minutes. Using a layer-by-layer method you can solve each piece one at a time in the first two layers, then learn 4 algorithms to fix the last layer (not necessarily in this order):

1) Rotate edges
2) Rotate corners
3) Permute corners
4) Permute edges

Sometimes you will have to use an algorithm twice. Each algorithm takes about 10 moves, and at a slow speed of one move per second and a bit of luck you can solve the last layer in under a minute. Here's a beginner's guide:

http://peter.stillhq.com/jasmine/rubikscubesolutio n.html [stillhq.com]

If you want to get faster you need to learn more algorithms so that you can complete two steps at once.

A popular method which can be used to get very fast times is the Fridrich method, but it requires a lot of memorisation and lots and lots of practice:

http://www.ws.binghamton.edu/fridrich/cube.html [binghamton.edu]

Personally I managed to get times of under 1 minute by practising the cube every day in the bus to and from work.

I noticed in the 4D model that elements disappear and reappear with each move. What's up with that?

You just cannot see all sides of the cube simultaneously, just as with it's 3d-counterpart.

If you exist in one dimension, is the 2nd dimension neccessarilry width, or is it height? There are many other choices, but we tend to pick time because it is easily understood by us.

It's a true 4 dimensional puzzle in the sense that this is what you could build as a rubik's cube equivalent if we lived in a 4d universe rather than a 3d universe.

The green cubes that appear and disappear as you make moves are from the 'hidden' face of the hypercube, which has 8 faces. Their projection is using a base unfolding, to understand what they've done consider the parallel from unfolding a 3d cube into 2d. Imagine you are staring precisely face on at a cube:

      XXX
      XXX
      XXX

Now unfold all the sides connected to the X's so you can see them straight on:

      OOO
      OOO
      OOO
AAAXXXBBB
AAAXXXBBB
AAAXXXBBB
      MMM
      MMM
      MMM

If you started playing a game of rubik's cube on this, you'd soon see another letter show up whenever you made a move, let's call it G for green. Where do the G's come from? From the sixth face of the cube that wasn't visible due to the choice of unfolding. The face exactly opposite of the X's ... the 'rear' of the cube if you will.

Same thing in the 4d case. There are 8 faces, only 7 of which are visible due to their poor choice of unfolding technique.

Here's wolfram's hypercube page for more info:
http://mathworld.wolfram.com/Hypercube.html [wolfram.com]

When they say 4D they actually mean 4 spatial (geometrical) dimensions.
Although time is said to be the 4th dimension is time, it is only an analogy. Time appears in several physical equations in a context similar to the 3 spatial dimensions, but it is always treated differently.
For example, the spacetime "distance" is calculated by:
sqrt(x^2+y^2+z^2-c^2*t^2)
Notice the negative sign and the additional speed-of-light factor.

If there were 4 spatial dimensions, the distance would be calculated by
sqrt(x^2+y^2+z^2 + v^2)
taking v as the displacement in the 4th dimension.

The Rubik's cube programs work by projecting 4 or 5 dimensions onto a 2 dimensional plane (your screen), basically in the same way that perspective is used to project 3D pictures onto 2D planes.

So the 4th and 5th dimension aren't mathematically or conceptually different to the familiar 3 dimensions. The only difference is that we cannot comprehend them.

it's pretty simple, really. Y'know how we draw a cube in 2D as two squares with the corners connected?
You can 'draw' a 4D cube in 3D space by making two wireframe cubes, and joining all the equivalent corners. You can also think of it as a cube moving from one place to another, with every 'frame' inbetween shown.