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 Post subject: CEF-turning platonics
PostPosted: Sun Jun 24, 2012 1:30 pm 
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I was wondering: how many of the regular platonic forms have been made with corner-, edge- *and* face-turning capabilities combined? Which ones? What are they called? Who made them? Which ones (if any) are still missing? Can they be made? Who will make them?

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 Post subject: Re: CEF-turning platonics
PostPosted: Sun Jun 24, 2012 3:06 pm 
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They only puzzle that comes to mind is Eric Vergo's Ultra-X viewtopic.php?t=19090 It has hexhedral, octahedral, and rhombic dodecahedral axes systems. But it doesn't strictly fit your requirements of being a platonic solid because it's a cuboctahedron not a cube or octahedron so it's a shape mod of what you want.

If you do want more shape mods, I suppose you could include a couple of the Dayan Gems, Clay n Eva's Concept 11, and Eitan's Comboctahedron as being shape mods of a tetrahedron.
Tetrahedrons have the advantage that face and vertex turns are basically the same so they should be easier to make. I can't think of any non shape mods that fit the requirements, but that could just be my memory failing me.

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 Post subject: Re: CEF-turning platonics
PostPosted: Sun Jun 24, 2012 4:35 pm 
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Wow, so what's the answer to my last question? :wink:

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 Post subject: Re: CEF-turning platonics
PostPosted: Sun Jun 24, 2012 8:08 pm 
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KelvinS wrote:
Wow, so what's the answer to my last question? :wink:

The Alphaminx through Epsilominx will satisfy all of the CEF-turning platonics. However, they are shape-mods.

To answer your last question, I might make them all... (I might be sick of the series by the Gammaminx, so we'll see. :lol: )

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 Post subject: Re: CEF-turning platonics
PostPosted: Mon Jun 25, 2012 9:21 am 
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By my calculations, there are at least 80 distinct CEFT Cubes assuming a combination of puzzles that have only one type of cut(2 FT Cubes * 5 CT Cubes * 8 ET Cubes). The number is probably even greater, since combinations are likely more sensitive to cut-depth differences.

For example, the 3*3*3 can have anything from infinitesimal outer layers an a huge center slice to huge outer layers and an infinitesimal center slice(zero center slice makes it a 2*2*2). By itself, this variation in cut depth for the 3*3*3 is only cosmetic. However, a Helicopter Cube + Skewb + 3*3*3 probably has several variations based on the 3*3*3's cut depth.

For the record, I based my counts for CT and ET Cubes on wwwmwww's animations in this thread, which also do an excellent job of illustrating how cut depth effects the resulting puzzle. I am also counting the 2*2*2 and 3*3*3 has distinct FT cubes.

The full series of CEFT Dedecahedrons would be even more difficult to enumerate.

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 Post subject: Re: CEF-turning platonics
PostPosted: Mon Jun 25, 2012 9:39 am 
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I wanted to answer something similar to Jeffrey but he saved my time. Thank you.
But I want to add something. Your calculation estimates only the number of puzzles when only plain cuts are allowed. With round cuts the number increases.

Before someone makes a CEF dodecahedron the CE-dodecahedron has to be made because that one is missing too.


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 Post subject: Re: CEF-turning platonics
PostPosted: Mon Jun 25, 2012 10:05 am 
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Jeffery Mewtamer wrote:
By my calculations, there are at least 80 distinct CEFT Cubes assuming a combination of puzzles that have only one type of cut(2 FT Cubes * 5 CT Cubes * 8 ET Cubes). The number is probably even greater, since combinations are likely more sensitive to cut-depth differences.
I believe it's going to be more complicated than that. For example, there's at least 4 ways to combine a Compy cube and a 3x3.

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