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Octoid
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Three axes with 180° turns each in a doctrinaire puzzle.

The Octoid has 3 turning axes, which lie on the short edges of the puzzle. These pass through the origin of the puzzle. Many stored cuts are present to ensure that no turns are ever blocked, and every piece can be separated from its neighbors after some turns. This puzzle has a total of 56 pieces, of which almost half of them are those tiny triangles around the octagons.

The base solid can be thought of as a distortion of a platonic octahedron. Of the (infinitely) many sweet spots for this distortion, this was the only one where leaving it as the base shape gave a practically workable new puzzle. If one chooses another sweet spot for the distortion, the result would be Krystian’s Twist. Please refer to the separate entry. Other sweet spots can be utilized, but the shape will have to be modified to make the proportions more practical.

Like the Krystian’s Twist, the Octoid also has jumbling capabilities. However, it’s quite restricted, so the only moves you can make (apart from reversing the moves) leads to a 7 move sequence that results in the shape being restored. Image 9 shows this result.

Without the jumbling turns this puzzle has 12290310144000000 permutations.
With jumbling turns the number is fourfold.

Edge length (long): 68 mm
Edge length (short): 37 mm

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