Hollow Mystery
Channel: OskarPuzzle
Date: 2019-07-13

More OskarPuzzle at https://www.youtube.com/OskarPuzzle?sub_confirmation=1. Buy at https://i.materialise.com/en/shop/item/hollow-mystery or at https://www.shapeways.com/product/4BJ8LVFWT/hollow-mystery. Hollow Mystery is a hollow Jaap's Sphere version of Rocket Twist, illustrating its unique geometrical properties. The puzzle has three squares, four triangles and three "diangles" wrapped around a sphere. At its initial state, the puzzle has three rotation axes, each 10.8122 degrees north of the equator, and equally spaced around the north-south axis. The puzzle has three main cuts, which is the south pole revolved around each of the three rotation axes. Hence the three cuts intersect at 120 degrees at the south pole. One of the triangles is centered at the north pole. The other three triangles are surrounding the south pole, bound by the three main cuts and three stored cuts.

Hollow Mystery has the unusual property that its rotation axes are not stationary, but they move around. When one side is rotated by 144 degrees over rotation axis no.1, then rotation axis no.2 remains, but rotation axis no.3 disappears. This is usual behaviour for a jumbling puzzle. However, when next a rotation of a side is made by 144 degrees over rotation axis no.2, then rotation axis no.3 reappears at a different location, at 72 degrees from its original location. With other combinations of rotations, also axes no.1 and no.2 moved around the sphere.

A consequece of the moving axes is that the puzzle can not be built with a classic shells mechanism and screwed-in axes. This also means that the puzzle cannot be fully modeled in e.g. pCubes. This puzzle may the first of its kind with this axes-than-move-around property.

The puzzle is definitely a jumbling puzzle, as it cannot be unbandaged into doctrinaire puzzle. The puzzle is also definitely quasi-doctrinaire, as any state of the Rocket Twist (or Hollow Mystery) is at most one turn away from a "rocket-shape" state. It is undetermined whether the puzzle is deeper-than-origin, as the moving-around of axes happens both when the puzzle is played shallowed-than-origin and deeper-than-origin.

Bonus facts:
-Six squares of Hollow Mystery can be assembled into a cube. It does not turn then, of course.
-The ten parts of Hollow Mystery can be assembled in an alternative way that does not turn either.
-All rotations are multples of 72 degrees (360 / 5), and the geometry features three pentagons.
-The geometry of the puzzle is sort-of dual to that of Fairly Twisted.

Question:
-Can this geometry be considered a quasi christal on a sphere?

Copyright (c) 2019, M. Oskar van Deventer.

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