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Triple Bandaged 3x3x3
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A 3x3x3 bandaged with three 1x2x2-blocks, placed parallely to each other.

This bandaged 3x3x3 is very close to the Big Block but splits that block into three equally sized blocks.
This split up creates a radical difference between the variants. The Triple has 28217548800 permutations (assumed that blocks are alway in the same place). The Big Block has 73483200 permutations which is smaller by a factor of 384. The Triple allows the edges to be flipped and to exchange two corners. Both is impossible on a Big Block.

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