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 Post subject: Snub Hexahedron 3x3x3
PostPosted: Thu Jun 04, 2009 12:19 pm 
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Just another truncation mod. :P
Some months ago, I had the (quite obvious) idea for this puzzle.
I searched whether somebody has done it before and wondered why I haven't found any.
I learned it the hard way.
I don't know, whether you can see it, but this mod doesn't change shape.
Maybe I can find some "In Progress"-pictures...


Attachments:
SnubHexahedron (0).JPG
SnubHexahedron (0).JPG [ 95.4 KiB | Viewed 3646 times ]
SnubHexahedron (1).jpg
SnubHexahedron (1).jpg [ 113.46 KiB | Viewed 3640 times ]
SnubHexahedron (2).JPG
SnubHexahedron (2).JPG [ 90.37 KiB | Viewed 3642 times ]
SnubHexahedron (3).JPG
SnubHexahedron (3).JPG [ 91.43 KiB | Viewed 3640 times ]
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 Post subject: Re: Snub Hexahedron 3x3x3
PostPosted: Thu Jun 04, 2009 12:31 pm 
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wow :shock:

I like it

It´s a different 333 mod..... a crazy mod

nice work Andreas¡¡¡¡¡

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 Post subject: Re: Snub Hexahedron 3x3x3
PostPosted: Thu Jun 04, 2009 2:22 pm 
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Wow, that's a cool idea. If you can hook up with Dr. Sticker for a set, you'll have yourself a really sweet puzzle!


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 Post subject: Re: Snub Hexahedron 3x3x3
PostPosted: Thu Jun 04, 2009 2:57 pm 
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wait what??!

crazy looking mod you got there Andres! I wouldnt have thought of that

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 Post subject: Re: Snub Hexahedron 3x3x3
PostPosted: Thu Jun 04, 2009 4:11 pm 
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Wow. Is that the first snub modification?

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 Post subject: Re: Snub Hexahedron 3x3x3
PostPosted: Thu Jun 04, 2009 4:21 pm 
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That is definitely the most complex truncation mod I've ever seen for a 3x3. I was looking at it for a few minutes before I could even understand how it works!


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 Post subject: Re: Snub Hexahedron 3x3x3
PostPosted: Thu Jun 04, 2009 5:05 pm 
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Very interesting shape. I like the way the area around the centres has a twisting effect applied to it.

Are you going to make the mirror-image version with the twists in the opposite direction?


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 Post subject: Re: Snub Hexahedron 3x3x3
PostPosted: Thu Jun 04, 2009 8:22 pm 
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I'm curious as to what it looks like scrambled.


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 Post subject: Re: Snub Hexahedron 3x3x3
PostPosted: Thu Jun 04, 2009 9:39 pm 
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I sort of like the pointy stickers on this mod(they could use some perfecting though.) I love how it doesnt shapshift, even though it looks like it should.

It reminds me of the icosahedron sticker wise. http://twistypuzzles.com/cgi-bin/puzzle.cgi?pkey=646

It doesn't look like the hardest truncation mod ever though. Oh wait, yes it does. :lol:

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 Post subject: Re: Snub Hexahedron 3x3x3
PostPosted: Fri Jun 05, 2009 10:55 am 
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Thank you everyone for all the praise.
Steryne wrote:
Wow. Is that the first snub modification?
As far as I know: Yes.
Justin wrote:
Are you going to make the mirror-image version with the twists in the opposite direction?
Definitely not!

BTW: This was the first step:


Attachments:
Snub Hexahedron (6).jpg
Snub Hexahedron (6).jpg [ 273.76 KiB | Viewed 3680 times ]
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 Post subject: Re: Snub Hexahedron 3x3x3
PostPosted: Fri Jun 05, 2009 11:46 am 
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WTF is that?!?! I use a ruler and a scribe! :lol:


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 Post subject: Re: Snub Hexahedron 3x3x3
PostPosted: Fri Jun 05, 2009 2:09 pm 
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:shock: Wow. I don't 7th grade math covers that stuff. :lol:


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 Post subject: Re: Snub Hexahedron 3x3x3
PostPosted: Fri Jun 05, 2009 3:23 pm 
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Wow, I can't believe that much went into this puzzle!!

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 Post subject: Re: Snub Hexahedron 3x3x3
PostPosted: Fri Jun 05, 2009 5:13 pm 
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Am I the only one that miscuts and makes something of it? I'll have to call up Einstien to help me make my snubbed tetrahedron!

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 Post subject: Re: Snub Hexahedron 3x3x3
PostPosted: Fri Jun 05, 2009 5:22 pm 
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Steryne wrote:
Am I the only one that miscuts and makes something of it? I'll have to call up Einstien to help me make my snubbed tetrahedron!

The icosahedron is actually a snub tetrahedron.

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 Post subject: Re: Snub Hexahedron 3x3x3
PostPosted: Fri Jun 05, 2009 5:37 pm 
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:| :roll: I knew that. Sorry Einstien.

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 Post subject: Re: Snub Hexahedron 3x3x3
PostPosted: Sat Jun 06, 2009 12:15 am 
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I only see Pythagoras' theorem and a system of equations. Sure, it takes a lot of work and some thinking (geometry) to set it up, but it shouldn't be that difficult to understand once it's done. Or am I missing something? :?


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 Post subject: Re: Snub Hexahedron 3x3x3
PostPosted: Sat Jun 06, 2009 3:32 am 
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Maybe not everyone has seen that but the 32 triangles are regular. And the squares belong to the original cube.
To achieve this you have to work out the exact cuts.
(or look them up: The solution is given on that sheet.)
Nothing more than a system with three equations and 3 variables...
Because of the square roots I didn't got beyond some implicit equations with 2 variables. Finally I solved these with brute force.
Maybe I have missed an easier way to calculate the cutting points. Does anybody know one?


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 Post subject: Re: Snub Hexahedron 3x3x3
PostPosted: Sat Jun 06, 2009 9:41 pm 
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Sometimes when I look at a puzzle, all I can do is :shock: :shock: :shock: :shock:
Great Job!


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 Post subject: Re: Snub Hexahedron 3x3x3
PostPosted: Sat Jun 06, 2009 11:20 pm 
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What makes something a snub model?

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 Post subject: Re: Snub Hexahedron 3x3x3
PostPosted: Sat Jun 06, 2009 11:43 pm 
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A snub polyhedron is made by adding triangles around each vertex. For the snub cube, this means adding 4 triangles per vertex or 32 triangles total.

Also, I realized I never complimented Andreas on this amazing cube! :)

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 Post subject: Re: Snub Hexahedron 3x3x3
PostPosted: Sun Jun 07, 2009 2:34 am 
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Danny Devitt wrote:
Also, I realized I never complimented Andreas on this amazing cube! :)


I think I commited the very same offense :oops:

Anyway, I like it, especially the fact the pieces are not symmetrical but the cube still doesn't change shape.

As for the easier way of calculating the sides, the answer is usually the same :wink: This one works, too. Some may think that is cheating, though :lol:


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 Post subject: Re: Snub Hexahedron 3x3x3
PostPosted: Sun Jun 07, 2009 3:04 am 
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Alex wrote:
As for the easier way of calculating the sides, the answer is usually the same :wink: This one works, too. Some may think that is cheating, though :lol:

Both of those are often very useful, but my new favorite thing to mess around with is this. Sometimes the program is pretty unhelpful, but you have to remember that it hasn't even been online for a month yet. I recommend watching the overview video as it shows you just how much useful (and useless, but cool) things it can do.

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 Post subject: Re: Snub Hexahedron 3x3x3
PostPosted: Sun Jun 07, 2009 6:34 am 
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I forgive you Alex and Denny.
And yes. I consider that cheating. :lol:
InProgress-Pictures anybody?


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 Post subject: Re: Snub Hexahedron 3x3x3
PostPosted: Sun Jun 07, 2009 9:43 am 
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Andreas Nortmann wrote:
InProgress-Pictures anybody?


Well, I don't have any at hand right now, but you can post yours if you wish :wink:


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 Post subject: Re: Snub Hexahedron 3x3x3
PostPosted: Sun Jun 07, 2009 4:23 pm 
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I'm very impressed at the fact that you tried making a shape mod in the shape of a snub cube, because, unlike most other regular and semiregular polyhedra, the side length and the volume and "diameter" are not linked by a few simple square roots. Instead to get the precise relations you need to solve a cubic equation! I ran into this problem a few years ago when trying to calculate the volume of the snub cube. Wikipedia has this to say:
Wikipedia wrote:
Cartesian coordinates for the vertices of a snub cube are all the even permutations of
(±1, ±ξ, ±1/ξ)
with an even number of plus signs, along with all the odd permutations with an odd number of plus signs, where ξ is the real solution to
ξ^3+ξ^2+ξ=1,
which can be written
ξ = (cbrt(17 + 3 sqrt(33)) - cbrt(-17 + 3 sqrt(33) - 1)/3
or approximately 0.543689.

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 Post subject: Re: Snub Hexahedron 3x3x3
PostPosted: Sun Jun 07, 2009 4:30 pm 
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Einstein, we may need you after all.

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 Post subject: Re: Snub Hexahedron 3x3x3
PostPosted: Sun Jun 07, 2009 11:10 pm 
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Steryne wrote:
Einstein, we may need you after all.

As I posted above, all you need is Wolfram|Alpha.

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 Post subject: Re: Snub Hexahedron 3x3x3
PostPosted: Mon Jun 08, 2009 11:39 am 
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Thanks qqwref.
And here we go for the "making of":


Attachments:
Snub Hexahedron (1).JPG
Snub Hexahedron (1).JPG [ 95.13 KiB | Viewed 3634 times ]
Snub Hexahedron (2).JPG
Snub Hexahedron (2).JPG [ 94.56 KiB | Viewed 3635 times ]
Snub Hexahedron (3).JPG
Snub Hexahedron (3).JPG [ 95.93 KiB | Viewed 3634 times ]
Snub Hexahedron (4).JPG
Snub Hexahedron (4).JPG [ 94.3 KiB | Viewed 3634 times ]
Snub Hexahedron (5).JPG
Snub Hexahedron (5).JPG [ 98.37 KiB | Viewed 3634 times ]
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 Post subject: Re: Snub Hexahedron 3x3x3
PostPosted: Mon Jun 08, 2009 12:04 pm 
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Thanks for the Making Of...

Now I have understand the cuts. Great work!!!!


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 Post subject: Re: Snub Hexahedron 3x3x3
PostPosted: Mon Jun 08, 2009 3:59 pm 
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I understand the cuts a lot better after seeing those pictures!

In the second "making of" picture there's another puzzle in the background. Looks like a 3x3x3 icosahedron :)


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 Post subject: Re: Snub Hexahedron 3x3x3
PostPosted: Tue Jun 09, 2009 5:15 am 
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qqwref wrote:
I'm very impressed at the fact that you tried making a shape mod in the shape of a snub cube, because, unlike most other regular and semiregular polyhedra, the side length and the volume and "diameter" are not linked by a few simple square roots. Instead to get the precise relations you need to solve a cubic equation! I ran into this problem a few years ago when trying to calculate the volume of the snub cube. Wikipedia has this to say:


You do not need to solve those cubic equations exactly to make a puzzle. Some numeric solution will give you a close enough approximation. Even if you had the exact solution would it really make the puzzle more accurate and easy turning? :wink:

Per

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