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Dittominx
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A hybrid axis system with turns that allow more than geometry dictates.

This puzzle has the shape of the deltoidal icositetrahedron, a catalan solid with 24 sides.
All of the 18 fourfold corners have one axes of rotation and each allow 90 degree turns. This is highly unusual as the axis system is equivalent to the hybrid of face and edge turning hexahedron. In such a geometry the edge turns usually allow only 180 turns. Despite this enhanced turning capabilities the puzzle is neither jumbling nor fudged.
The cuts are so shallow that two adjacent turns (which are never of the same set of turns) share only one piece per pair.
The inventor stickered it with 12 different colours.

Compared with the number available if the puzzle can be disassembled and reassembled there are these restrictions:
-The edges can't be oriented.
-The orientations of fourfold tips and permutations of edges must have the same parity.
Stickered as shown here the puzzle has 9500068070689996800000 = 9.5 *10^21 permutations.

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