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Alternating Asynchronous Antislice Face Turning Octahedron
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A FTO which enforces heavy restrictions on the puzzle.

The name basically describes the movement of the puzzle. It moves just like a face turning octahedron except one can only make certain moves at any given time. At the start, one can only make clockwise moves by one step and after that, the only way to scramble it further is to move the opposite side also by one step. This is why the inventor calls it asynchronous antislice as opposed to just antislice as the opposing move can be done asynchronously and aren't directly geared together. See images 2-3.
After that, the alternating part of the name comes in, because now one can only move faces one step counter-clockwise, and the opposite face also has to be turned counter-clockwise, bringing it back to the original state where faces can be moved clockwise. Image 4 shows the result of such a move.
When the puzzle is in the base state (any face can be moved clockwise), the positions of the edges from the group PSL(2,11), each of the two orbits of 12 face centers also form PSL(2,11), and the positions of the six corners (ignoring orientation) form Alternating(5) just as in the alternating skewb.
Edge length: 73 mm
Weight: 78 grams

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