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Mirror 2x2x3 Floppy I-cube
Above:Solved
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A 3x3x3 bandaged in two dimensions a successively bumped.

First this puzzle looks like the "Bump Tower Cube" (see the separate entry) but this is not a 2x2x3 but a 3x3x3. It was bandaged not as an I-Cube (as the name suggest) but to resemble a 2x2x3. Therefore the pieces were bandaged in two dimensions.
In additiona to the bandaging the puzzle was bumped, meaning it was truncated on one plane but elongated on the opposite. This is repeated for the other two dimensions.

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