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Three axes with 180� turns each in a doctrinaire puzzle. With one piece type more than the octoid.
The Heptoid is a 3-axes deepcut puzzle that turns in increments of 180�. This puzzle is related to the inventor's previous Octoid, but features heptagons instead of octagons on the surface of the puzzle. This was achieved by adjusting the angle that the 3 axes are "raised up" from a flat plane. On the Octoid, they are about 26.2 degrees, whereas on the Heptoid they are about 14.9 degrees raised up from the plane.
This puzzle shares many piece types with the Octoid, and the only pieces that are unique to each puzzle are the small triangles that surround the central polygon.
The external shape is similar to Oskar's Hepta Twist.
Like the Octoid, the Heptoid can jumble. The angle is about 47.98 degrees. A closed form is unknown so far. See image 8. But the only thing you can do with the jumbling is to do a 7 turn sequence that restores the shape.
Height: 67 mm
The puzzle has 439022168653824000000 = 439*10^18 permutations if all pieces are considered distinguishable. Due to the limited number of moves it has a huge number of restrictions:
-The orientation of the last heptagon is determined by the first two.
-The large triangles are not orientable.
-The non-equilateral triangles are split into three sets. None or two of these sets can have odd permutations.
-The corners are split into three sets. None or two of these sets can have odd permutations.
-The small triangles are split into three sets. All sets always have even permutations.
-The parities of the three set of non-equilateral triangles are determined by the orientation of the edges.
-The parities of the three set of corners are determined by the orientation of the edges.
-The permutations of the heptagons and the orientation of the edges have the same parity.
-The permutations of the large triangles and the orientation of the edges have the same parity.
-The permutations of the heptagons determine the permutations of the last three large triangles and vice versa.
-These restrictions multiply up to a factor of 43008.
Stickered as shown here the puzzle has 5184974592000000 = 5.18 *10^15 permutations.
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Heptoid
