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Showing all parities in the 3x3x3 super cube. A 3x3x3 which has the same number of permutations as the super 3x3x3 and is always solvable after arbitrary reassembling.
There are five types of parity restrictions to a super 3x3x3:
1. Permutation of Edges
2. Permutation of Corners
3. Orientation of Edges
4. Orientation of Corners
5. Orientation of Centers (Including 90-degree turn only)
When a super 3x3x3 (with visible orientations of the faces) is disassembled and reassembled without taking care about the configuration there is a probability of only 1/24 to achieve a solvable permutation.
In this case the stickering of a mass produced 3x3x3 was modified
1. to make the orientations of the faces visible
2. to create a variant that is always solvable after arbitrary reassembling.
This variant has the same number of permutations as the super 3x3x3.
Please note that there is a pair of identical edges AND a pair of identical corners. On a non-super 3x3x3 one pair would have been sufficient but since there are no identical faces two pairs are necessary.
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Thank you to the following people for their assistance in helping collect the information on this page: ChoongMyoung Lee.
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