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An edge-turning hexagonal dipyramid sliced through the origin.
Dave's Diamond is a hexagonal dipyramid, shaped such that slice planes at a certain angle through the origin of the puzzle have four-way symmetry. Each of the 12 resulting axes can turn in increments of 90 degrees. But when the puzzle is shape-shifted, only half of the axes remain available for turning. This set of axes are all at right angles to each other, so that Dave's Diamond can be thought of as two overlapping but rotationally offset 2x2x2 cubes.
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