After some more time I finally would like to present Sphere 612. As the name says, it is gelatinbrain's 6.1.2. I actually think it is fine as a name. Many will probably disagree as it is a terrible name. But I want it to be a tribute to gelatinbrain's idea. It is not as straight foreward to think up as a platonic solid with a certain depth of cut about vertice, edge or face.
Sphere 612 has very shallow cuts, which itself is not a problem. However since there are cutplanes through all the pieces at angles of 45° as well, there wasn't much choice of how deep the shell needed to be.
Deeper shell results in very small hidden corner pieces (those that are infact attached to the core). Shallower resulted in smaller feet of the 48 small triangles.
The first version worked well but was a little loose and way to small for my likes and stability. So a second version was created. The first small one actually has a larger diameter of a normal 3x3x3 cube (60mm) but appears MUCH smaller due to the spherical form. The second one is 75mm which sounds large but is a good size for the puzzle.
PROBLEMS WITH THE DESIGN:
Breakin in of the second version took a loooong time. It didn't move at all at first. I think the problem is the fixed corner pieces. They can't "sink" into the core during the breaking in process. All other pieces have a tolerance to the surface of the spherical core and during breaking in the tension is adjusted. The corner pieces start being more and more of a bump during the turns.
Still I wonder if loose corner pieces that are just hidden in there would do for better stability. Maybe someone has experience to tell? I would greatly apreciate advice.
Stickering the faces is difficult. I tried a big patch and it was horrible. I tried an outline but it didn't work either. I then cut small circles and they are still to big to cover the curviture. Maybe with a hair dryer it would work?
goes to Olivér for the beautiful stickers and NXTgen for discussing the mechanism a little, even though I didn't listen to his advice in the end.
And of course to gelatinbrain for his gelatin brain.
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Mixed up a little with shape change but WITHOUT jumbling (this is what you can do with gleatinbrain's applet):
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Mixed up to same degree WITH jumbling (the bottom and right face are blocked, which does not happen in the applet):
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Size comparison of 57mm cube, 60mm sphere and 75mm sphere:
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artistic still life:
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