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Mystic Stone
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A jewel-like shape of the Hexcopter 12.

This is the first out of a planned series of seven puzzles, called Mystic. All seven will implement the same jumbling only axis system: face turning hexagonal dipyramid. Each puzzle of the series introduces at least one piecetype that the previous puzzle did not have. The Mystic Stone implements the first 3 piecetypes (excluding the core).
The Mystic Stone is a jumbling puzzle. It has 18 faces and 18 different colours. There are 31 mathematical pieces, including the core. 12 of these pieces do not permute around the puzzle - they can only be spun in place. The remaining 18 pieces can all swap locations and they are all the same shape. This is remarkable because they are not all in mathematically equivalent locations in the solved shape. In fact, it might be more technically to correct to say there are 4 types of pieces present, but 2 of these types are identical. Were the puzzle cut deeper, these two types of pieces would diverge and no longer look identical.
Each of the 12 grips (around the corners without top and bottom) can reach 5 different jumbling stops, including the position they start in. These stops are approximately at 104.5�, 151.0�, 209.0�, and 255.5�, in addition to the natural stop at 0�. These angles can be expressed precisely as �acos(-1/4) and �acos(-7/8). This puzzle only implements the first layer of jumbling.
Solvingwise it is a reimplementation of Hexcopter 12.

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