Yes, you could represent the 4D cube state textually too (I think this is what you are asking). However, the 4D cube does not have 27 sides (also called "faces"). It has 8 faces with 27 stickers per face, verses the 3D cube which has 6 faces with 9 stickers per face. So a textual representation of the 4D cube might be something like...
Face 1: (RRR/RRR/RRR)/(RRR/RRR/RRR)/(RRR/RRR/RRR) Face 2: (GGG/GGG/GGG)/(GGG/GGG/GGG)/(GGG/GGG/GGG)
... Face 8: (BBB/BBB/BBB)/(BBB/BBB/BBB)/(BBB/BBB/BBB)
And a twist would jump all the characters representing stickers from certain faces to others in a certain way. If we represent the puzzle in this way, a twist is probably more difficult to follow than the graphically projected representation of MagicCube4D though.
I've seen textual representations that try to mimick mathematical projecting down dimensions too. These are more complicated in their organization but still contain the same total number of characters representing all the different colored stickers.
Sorry to be the annoying stickler. That is not a 2D Rubik's cube, but rather 1 face of a 3D Rubik's cube. To correctly make the analogy, you need to reduce all parts of the puzzle by a dimension. So for a 2D Rubik's cube, the 2D faces of the 3D version become 1D, and the 2D stickers of the 3D version also become 1D.
But you were right that it can't be scrambled and is always solved.
Thought you might be interested to know...
MagicCube4D supports 2x2x2x2, 3x3x3x3, 4x4x4x4, and 5x5x5x5 puzzles.
MagicCube5D supports 2x2x2x2x2, 3x3x3x3x3, 4x4x4x4x4, and 5x5x5x5x5 puzzles.
You can buy a 5x5x5 Professor's cube from www.mefferts.com.
These puzzles are true higher dimensional analogs. Every characteristic of MagicCube4D is "upped" a dimension from the original puzzle. For example, on the 3D cube stickers are 2D, but on the 4D cube, stickers are 3D. This is also true for the puzzle "faces".
Have we really added a dimension? Well, perhaps not because the higher dimensional portions of the puzzle are being projected down to our real lower dimensions. So in a sense, yes these are just "more complicated 3D puzzles". But they are not just puzzles that are more complicated in some arbitrary way like adding more stickers. There are more complicated in a way that preserves analogies to what a 4D Rubik's cube would be like in higher-d spaces (if those could exist).
I find the best way to think about things is by "dimensional analogy". Think about how a 3D cube would look to a 2D being (you'd have to project the puzzle into the 2D world to even see it), and then the ideas behind MagicCube4D start making sense. Try to draw a Rubik's cube on a flat sheet of paper and you'll see what I mean.
Slashdot Mirror
Face 1: (RRR/RRR/RRR)/(RRR/RRR/RRR)/(RRR/RRR/RRR)
Face 2: (GGG/GGG/GGG)/(GGG/GGG/GGG)/(GGG/GGG/GGG)
Face 8: (BBB/BBB/BBB)/(BBB/BBB/BBB)/(BBB/BBB/BBB)
And a twist would jump all the characters representing stickers from certain faces to others in a certain way. If we represent the puzzle in this way, a twist is probably more difficult to follow than the graphically projected representation of MagicCube4D though.
I've seen textual representations that try to mimick mathematical projecting down dimensions too. These are more complicated in their organization but still contain the same total number of characters representing all the different colored stickers.
Hope this helped answer your question.
Sorry to be the annoying stickler. That is not a 2D Rubik's cube, but rather 1 face of a 3D Rubik's cube. To correctly make the analogy, you need to reduce all parts of the puzzle by a dimension. So for a 2D Rubik's cube, the 2D faces of the 3D version become 1D, and the 2D stickers of the 3D version also become 1D.
But you were right that it can't be scrambled and is always solved.
Here you go:
http://www.gravitation3d.com/magiccube5d/2d_rubik' s_cube.jpg
Thought you might be interested to know... MagicCube4D supports 2x2x2x2, 3x3x3x3, 4x4x4x4, and 5x5x5x5 puzzles. MagicCube5D supports 2x2x2x2x2, 3x3x3x3x3, 4x4x4x4x4, and 5x5x5x5x5 puzzles. You can buy a 5x5x5 Professor's cube from www.mefferts.com.
These puzzles are true higher dimensional analogs. Every characteristic of MagicCube4D is "upped" a dimension from the original puzzle. For example, on the 3D cube stickers are 2D, but on the 4D cube, stickers are 3D. This is also true for the puzzle "faces".
Have we really added a dimension? Well, perhaps not because the higher dimensional portions of the puzzle are being projected down to our real lower dimensions. So in a sense, yes these are just "more complicated 3D puzzles". But they are not just puzzles that are more complicated in some arbitrary way like adding more stickers. There are more complicated in a way that preserves analogies to what a 4D Rubik's cube would be like in higher-d spaces (if those could exist).
I find the best way to think about things is by "dimensional analogy". Think about how a 3D cube would look to a 2D being (you'd have to project the puzzle into the 2D world to even see it), and then the ideas behind MagicCube4D start making sense. Try to draw a Rubik's cube on a flat sheet of paper and you'll see what I mean.
There is an excellent FAQ about the puzzle on the superliminal site, which I recommend. http://www.superliminal.com/cube/FAQ.txt