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 Post subject: Piece sets of the 3x3x3
PostPosted: Fri Dec 04, 2009 10:45 am 
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Joined: Mon Aug 02, 2004 7:03 am
Location: Koblenz, Germany
Lately I have presented a concept of classifying puzzles by symmetry class and piece sets. This concept of piece sets can now be illustrated completely for the 3x3x3. The unmodified 3x3x3 has 3 types of pieces:
Corner, Edges and Faces.
Therefore we can derive 8 different mods from the 3x3x3:

{CEF} represents the unmodified 3x3x3
{CF} is implemented by the simple overlapping cube.
{CE} is implemented by the void cube. Thank you, Mr Okamoto.
{EF} is the edges-only-cube
{F} is the Babyface 1x1x1.
{E} is the edges-only-void-cube
{C} is the 2x2x2
{} is the 1x1x1

And here they are:
Attachment:
3x3x3CubieSets.jpg
3x3x3CubieSets.jpg [ 205.18 KiB | Viewed 1297 times ]

This picture was one reason (of two) for me to build the Babyface.

Who else has come how far in collecting this series?


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 Post subject: Re: Piece sets of the 3x3x3
PostPosted: Fri Dec 04, 2009 10:52 am 
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Joined: Sat Jul 11, 2009 1:09 pm
Location: My House
I've never really thought about this. This was really interesting to read. :D

Alex

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 Post subject: Re: Piece sets of the 3x3x3
PostPosted: Fri Dec 04, 2009 1:02 pm 
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Joined: Tue Jan 01, 2008 7:30 pm
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:mrgreen: I feel very honored!

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"I discovered the triangle one day while shaving. I trimmed my beard like the intersection of three circles and noticed how I could unfog a square in the bathroom mirror by rubbing my beard circularly against the glass."-Franz Reuleaux


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 Post subject: Re: Piece sets of the 3x3x3
PostPosted: Sat Dec 05, 2009 9:40 am 
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Joined: Mon Apr 03, 2006 10:38 am
Location: Connecticut
Hi Andreas,

I like your categorization and example set of puzzles. I have proposed a similar categorization - you can read about it here:
http://robspuzzlepage.com/rearrangement.htm#definitions

- scroll down to #5.

Your symbolism may be easier to follow, and you've also accounted for {}, the 1x1x1, which I did not include,
since I would term it "order 0" - nothing turns, and therefore it is not really a twisty puzzle.

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 Post subject: Re: Piece sets of the 3x3x3
PostPosted: Sat Dec 05, 2009 11:22 am 
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Joined: Mon Aug 02, 2004 7:03 am
Location: Koblenz, Germany
Tanner shall be honored as he deserves!!!

@Rob:
What a page! :shock:
I will need some time to consume that.
I find it quite interesting (because its like my approach!!) how you define "order" of a puzzle. Considering that I wondered why you haven't posted here:
viewtopic.php?f=1&t=15258


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 Post subject: Re: Piece sets of the 3x3x3
PostPosted: Mon Dec 07, 2009 12:33 am 
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Joined: Sun Nov 01, 2009 10:59 pm
Location: Blacksburg, VA
I like your classification method. Thanks for the pics for illustration!

Could a similar system be used to classify shape mods? Systems I can think of become quickly complicated.

i.e. using capital letters to imply that orientation matters, lower case to imply that it does not.

As far as shape/sticker modifications of the 3x3x3 go:

- the standard cube requires orientation of corners and edges, but not faces {CEf}

- a circle cube is functionally the same, but also requires orientation of faces {CEF}

- a mastermorphix requires center orientation, but now some of the corners require orientation, and others do not {c'EF}
I've used c' to represent an incomplete orientation requirement of corners. The problem here is that, at least to a limited degree, edges don't require permutation, and my system does not reflect that.

- likewise, a fisher cube requires orientation from corners, but only some edges and some faces {Ce'f'}

In any case, I appreciate the simplicity of you organization scheme, and I hope it sees a wide adoption.


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