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Rexoctahedron³
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A cuboctahedron that is face turning on both sets of faces, in this case with cuts resembling the 3x3x3 and the Rex Cube.

This is not the first hybrid that combines a face turning cube with a corner turning cube. Neither it is the first puzzle which does so in shape of a cuboctahedron (an archimedean solid) although there has been only one earlier, the 3x3x3 Rainbow Cube.
New in this puzzle are the exact cuts. One set is meant to resemble the Rex 3x3x3 which is not exactly true as the cuts of a Rex Cube cut the corner of a cube. In this cube the cuts run differently and thereby create a new puzzle.

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