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Three axes with 180� turns each in a doctrinaire puzzle. With one piece type more than the Heptoid.
This puzzle follows the Octoid and the Heptoid. The Enneoid has 3 rotation axes, 180 degree rotations, and deep cuts. The Enneoid is what the inventor considers as the limit of practicality for this series, as higher polygons would result in very large puzzles and/or very thin pieces. Even at this level it is already pretty large, at 89 mm from top to bottom. Thanks to the large flat sides it does not feel very big.
As with the preceeding puzzles, there are also jumbling turns (see image 7) which only allow a seven-turn sequence that goes back to the original shape. This puzzle contains all the pieces that the Heptoid does, with the addition of the 9 thin triangles around every enneagon, thus it can be considered a superset of the Heptoid.
This puzzle has the turning axes placed even closer to planar than the Heptoid, 11.6 degrees vs the Heptoid's 14.9 degrees.
This is the first twistypuzzle that features enneagonal pieces that can actually be scrambled. The earlier puzzles had enneagons as part of the core.
Height: 89 mm
The puzzle has 481650473726380718954643456000000000 = 482*10^33 permutations if all pieces are considered distinguishable. Due to the limited number of moves it has a huge number of restrictions:
-The nonagons allow only for three orientations.
-The orientation of the last nonagon is determined by the first two.
-The triangles27 (the smallest triangles) are split into three sets.
-The permutations of the triangles27 are always even.
-The pentagons are split into three sets.
-The permutations of all three sets of pentagons are always even.
-The corners are split into three sets.
-The permutations of the corners are always even.
-The triangles9 (outside of the nonagonal sides) are split into three sets.
-The permutations of the triangles9 are always even.
-The orientations of the edges determine the parity of the permutations of triangles27, triangles9 and corners. (factor=4^3)
-The orientations of the edges determine the parity of the permutations of nonagons and triangles4. (factor=2^2)
-The orientation of the last nonagon is determined by the permutations of triangles4. (factor=3)
Stickered as shown here the puzzle has 42483297216293240832000000000 = 42.5 *10^27 permutations.
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Enneoid
