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3D loopover

brododragon

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My idea is to get a hollow metal ball and 3D Print pieces of a sphere. You would assemble it around the ball. This would have the same turning idea as loopover.
 

Ben Whitmore

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Sep 28, 2019
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Loopover is a torus, not a sphere, and you'd have trouble building a physical version because the inner radius and outer radius are different, which would mean that some pieces would have to be different sizes and you wouldn't be able to do moves along one of the axes.
 

xyzzy

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Dec 24, 2015
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But a torus is a ring.
… Which is not a sphere, yes.

There have been quite a few puzzles where tiles can be moved in a loop:
(and a whole bunch more; you can see the whole list on Jaap's Puzzle Page)

However, these don't have the topology of the standard Loopover game (which is a torus), and it's simply not possible to embed a torus into a sphere. (A sphere's sides do "wrap around", but they wrap around in a different and incompatible way from how the torus's sides "wrap around".)
 

erictom333

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I have an idea for how to make a physical version of Loopover. Make a torus with 5 rings that rotate in the toroidal direction, make 5 grooves running in the poloidal direction where pieces can slide, and add in the pieces.
 

erictom333

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anyway, here's what my design for a 3D Loopover would look like. The poloidal rings of colored tiles rotate in the poloidal direction, and the toroidal rings (here pentagonal, but they should be circular) rotate in the toroidal direction.
looooopover.png
 
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erictom333

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The V-Sphere is a good starting place. You just remove the z-axis of turnability and it could theoretically work.
As already mentioned in this thread, Loopover is toroidal, not spherical, so that won't work. Also I don't think you even could make a V-Sphere with 3 or more layers per axis.
<snip> 15 puzzle cube </snip>
Not relevant, sorry.
 
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