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Babycross 4x4x4
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A 4x4x4 with four additional pieces on all six sides. All fully functional.

The additional puzzles were added with the same technique that was used to make 2x2x6s in the past: modifying the 4x4x4 centers to rotate freely.

The turning quality of the extensions is a little rough, although this is far preferable to loose extensions that allow the edge pieces to fall out.
The name comes from the puzzle's similarity to the babyface cube, and the cross cube. The added cubies also look like baby layers.

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