Although knowing how to solve it using the very basic method, which is the layer-order-method, I have come across other quicker methods out there, which are used in speed cubing and competitions.
I for one would be very interested in theoretically finding the best solution rather than creative methods.
Now for a 3X3X3 original Rubik's cube, its atomic structures can be categorized into 3 groups:
1. The Absolute Centers (having only one face/color)
2. The Relative Centers (having two faces/colors)
3. The Corners (having the most, three faces/colors)
If there is truly a theoretically fastest method out there, then I haven't really stumble upon one that would have the simplest teaching demonstration. This project is intended for such.
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This research begins now(Solving Cube with patterns as faces will need to be addressed later on):
All I know for now, is that the Absolute Centers are fixed. Hence, we can already tell which sides each 6 faces of the Cube should placed respectively.
A good aiding tool is the flash program of the cube located at this site:
http://www.pamlicobiz.com/games/cube.htm
I would love to find a standalone version.
Now I need to find the relationships between each of the 3 groups.
Now for the permutations of the Corners, are all 8! (factorial of 8) possible for the Cube? It seems so...