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A mixup cube with different cut depths on different axes.
This puzzle implements two different types of turns both resembling two preexisting Mixup puzzles. On two axes the turns are as deep as known from a Mixup plus cube. One the third axis the turns are wider, resembling a Son-Mum Cube. This combination of turns makes it act as a cuboid with only 180° turns on 4 faces, although still having the Mixup property of 45° turns on the slices.
This might not seem like a set up of possible turns, because of the different cut depths, and it normally isn't, but slight fudging allows it.
The fudging is so small that it has a perfect contact point in the middle of the pieces (edges and petals) and only curves away from each other at the corners. It doesn't matter though since the pieces never accidently turn in place. The large wedges cause bandaging but have a limited number of possible positions. Thin wedges cannot leave the Son-Mum layer.
This puzzle is named Column cube because it looks to the inventor similarly to old Roman columns.
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