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4 Corners Rotated
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A 3x3x3 truncated to give it the shape with an unusual symmetry group.

This puzzle is obviously a simple truncation of a 3x3x3. It was made for the sake of completing a series discovered only month ago.
There are 33 subgroups of the symmetry group of the hexahedron, including the two trivial subgroups. After scanning through his collection the builder discovered that he already owned 21 of these. Most of the missing ones are rather unsymmetric and near to the no-symmetry.
"4 Corners Rotated" was the exception: It is symmetric with respect to rotations around all four corners (which explains the name) but not to any mirrorings like the Half Truncated Cube or many other variants.
Up to this point no shape transformation with this symmetry was known.

In addition to its unusual symmetry this puzzle demonstrates a rarely used truncation technique: The corners are truncated irregularly. One dimension of the cut goes over the whole cube, the second goes over half of the cube and the third goes over only half a cubie.



Thank you to the following people for their assistance in helping collect the information on this page: Andreas Nortmann, Lawrence Cuthbert.

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