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 Post subject: All 33 subgroups of hexahedral symmetries
PostPosted: Sun Jan 13, 2013 11:20 am 
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Joined: Mon Aug 02, 2004 7:03 am
Location: Koblenz, Germany
Hi,

You know I am obsessed with completing serieses.
You know I am obsessed with symmetry.
Therefore I am obsessed with completing the series of shape variants for the octahedral symmetry.

For reading about the point symmetry group of the cube I suggest this page:
http://www.jaapsch.net/puzzles/symmetr1.htm
There can you read that there are 33 subgroups.
When I first recognized that a series of shape variants could be made out of these subgroups (two years ago) I scanned through my colletion and found out that I already had samples for one half of the elements.
As you can read in this entry I discovered at least one beautiful (my opinion) variant when I thought about the missing slots.
As you might see the degree of symmetry decreases when going downwards and therefore the variants get more abstract.

In this latest posting I presented the last four elements of this series which allowed me to complete the series.
Please note that I had to gimp four puzzles into the image because these four are stored in a different place.

Does anybody understand what I am talking about :?:
Does anybody want all the technical names :?:


Attachments:
36 SymmetryClasses.JPG
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 Post subject: Re: All 33 subgroups of hexahedral symmetries
PostPosted: Sun Jan 13, 2013 11:49 am 
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Joined: Thu Dec 02, 2004 12:09 pm
Location: Missouri
Andreas Nortmann wrote:
Does anybody understand what I am talking about :?:
Mostly... though I'm sure not close to the degree that you do. Symmetry is one of those subjects that has always fascinated me and it always seems the more that you understand the more you realize there is ALOT more to this subject then one initially thinks. Symmetry and Group Theory seem to be at the heart of Physics and I suspect we will always be learning new and interesting things here. But I digress...
Andreas Nortmann wrote:
Does anybody want all the technical names :?:
YES!!!! I for one certainly do.

Congrats on completing this series,
Carl

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 Post subject: Re: All 33 subgroups of hexahedral symmetries
PostPosted: Sun Jan 13, 2013 3:28 pm 
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Joined: Tue Apr 19, 2011 4:48 pm
Location: Germany
Hi Andreas,

congratulations on finishing the series! Which group is the next on your list?


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 Post subject: Re: All 33 subgroups of hexahedral symmetries
PostPosted: Mon Jan 14, 2013 11:35 am 
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Joined: Mon Aug 02, 2004 7:03 am
Location: Koblenz, Germany
Okay Carl,

In correct order there are:
sk1ED4ESKS; 3x3x3
sk2ED4KD; SnubCube
sk2ED4ES; SharpEdges 1810452882060 Dodecahedron
sk2ED4KS; Truncated Corners 000 011 101 110 - Mastermorphix
sk3ES390; SharpEdges 154000AA000 SharpOctahedron
sk4ED4; AsymCorners 40020060204000801090080010
sk4EDPSKS; Squished cube; Triagonal Trapezohedron
sk6ESPS90; SharpEdges C0C00000 Idiots Windmill
sk6ES290; SharpEdges 15400000168 (Cheops Cube was not available)
sk6ES2ZP; SharpEdges 5000082000 Xenomorphix
sk6ES3; SharpEdges 180600000 Rhombus Cube
sk6ZD3ZP; SharpCorners 8800101000
sk6ZD390; Milloctahedron
sk6ESPSKS; Truncated Corners 000 001 110 111 - Cushion Cube
sk8EDKD; SharpEdges 201040280040 Rhombohedron
sk8EDPS; SharpEdges 201100220100 IdenticalCircles
sk8EDKS; Truncated Corners 000 011 101
sk12ZD90; AsymCorners 84210
sk12ZDKS; SharpCorners 44000
sk12ZD3; AsymCorners 40020000000000000000080010
sk12ZDZP; AsymCorners 10400000000000004040000
sk12ES2; SharpEdges 28000 5-Sided Sharp Cube
sk12ESPS; SharpEdges 12000000 Skewed Cube
sk12ESKS; SharpEdges 10400000 DragonLike 1
sk12PSKS; OctagonalEdges 21E8A00145E10
sk12ZDKD; OctagonalEdges 21E0800104C84
sk16ED; SharpCorners 40000040010
sk24ZD; AsymCorners 4200
sk24KS; AsymCorners 200000004000
sk24ES; AsymCorners 4080
sk24PS; AsymCorners 200000000000000000004000
sk24KD; AsymCorners 800000004000
sk48; AsymCorners 4000

husotaso wrote:
Which group is the next on your list?
The same two groups as everytime: The unknown one and the secret one.
Seriously: I have a list of incomplete serieses and a list of puzzles I want to build in the future. There are entries on the second list which have been there for years.
I do not have a longterm plan. This is a hobby. I build want my feeling tells me to build.


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 Post subject: Re: All 33 subgroups of hexahedral symmetries
PostPosted: Mon Jan 21, 2013 2:40 pm 
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Joined: Sun Mar 02, 2008 11:33 am
Location: Hiram, Ohio
Andreas Nortmann wrote:
The same two groups as everytime: The unknown one and the secret one.
Seriously: I have a list of incomplete serieses and a list of puzzles I want to build in the future. There are entries on the second list which have been there for years.
I do not have a longterm plan. This is a hobby. I build want my feeling tells me to build.


Andreas, you must be careful, if you complete even more series you might accidentally start existing on a higher plane of existence, thus becoming a sort of deity :)


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 Post subject: Re: All 33 subgroups of hexahedral symmetries
PostPosted: Tue Jan 22, 2013 11:24 am 
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Location: Koblenz, Germany
Hunter Palshook wrote:
Andreas, you must be careful, if you complete even more series you might accidentally start existing on a higher plane of existence, thus becoming a sort of deity :)

Improbable. That higher plane of existence is already blocked by other members. :x


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 Post subject: Re: All 33 subgroups of hexahedral symmetries
PostPosted: Tue Jan 22, 2013 11:50 am 
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Location: Bay Area, California
Andreas Nortmann wrote:
Hunter Palshook wrote:
Andreas, you must be careful, if you complete even more series you might accidentally start existing on a higher plane of existence, thus becoming a sort of deity :)

Improbable. That higher plane of existence is already blocked by other members. :x

Besides, (hyper)planes are so limiting. One should aspire to exist on other exotic surfaces besides just planes :wink:

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