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 Post subject: Adjacent PolyhedraPosted: Wed, 27 Jun 2012 19:08:45 UTC
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Joined: Wed, 4 Apr 2012 03:51:40 UTC
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Location: Hockeytown aka Detroit
We define polyhedra to be adjacent if the polyhedra have no common interior points and two faces (one on each polyhedra) intersect in a polygon that has positive area. Can polyhedra be arranged so that every pair is adjacent?

I tried generalizing the problem, said it was way too difficult, tried the 2D version of the generalization, and then thought I came up with what I believe is an intuitive proof for the 4 Color Theorem without using a computer (I still have no clue why my "proof" can't be made to be rigorous...). In short, any help would be appreciated.

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 Post subject: Re: Adjacent PolyhedraPosted: Wed, 27 Jun 2012 19:17:38 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12097
Location: Austin, TX
rdj5933mile5math64 wrote:
We define polyhedra to be adjacent if the polyhedra have no common interior points and two faces (one on each polyhedra) intersect in a polygon that has positive area. Can polyhedra be arranged so that every pair is adjacent?

I tried generalizing the problem, said it was way too difficult, tried the 2D version of the generalization, and then thought I came up with what I believe is an intuitive proof for the 4 Color Theorem without using a computer (I still have no clue why my "proof" can't be made to be rigorous...). In short, any help would be appreciated.

You're being too vague. If you want feedback on a purported "proof" you need to post it so we can point out where you've gone wrong.

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 Post subject: Re: Adjacent PolyhedraPosted: Wed, 27 Jun 2012 19:28:38 UTC
 Senior Member

Joined: Wed, 4 Apr 2012 03:51:40 UTC
Posts: 129
Location: Hockeytown aka Detroit
rdj5933mile5math64 wrote:
We define polyhedra to be adjacent if the polyhedra have no common interior points and two faces (one on each polyhedra) intersect in a polygon that has positive area. Can polyhedra be arranged so that every pair is adjacent?

I tried generalizing the problem, said it was way too difficult, tried the 2D version of the generalization, and then thought I came up with what I believe is an intuitive proof for the 4 Color Theorem without using a computer (I still have no clue why my "proof" can't be made to be rigorous...). In short, any help would be appreciated.

You're being too vague. If you want feedback on a purported "proof" you need to post it so we can point out where you've gone wrong.

Hmmmm I think I might try to look over the "proof" later today.~ I was actually more interested for help with the original problem.

The second paragraph was used more for describing the fact that I've tried the problem put and am not just flooding the board. If I still see no reason why the supposed proof is wrong I'll be sure to post it on the board tomorrow.

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math puns are the first sine of madness
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 Post subject: Re: Adjacent PolyhedraPosted: Thu, 28 Jun 2012 19:25:20 UTC
 Senior Member

Joined: Wed, 4 Apr 2012 03:51:40 UTC
Posts: 129
Location: Hockeytown aka Detroit
Sorry for double posting.

Hmmmz I think I have that the answer to the problem is that you can, I have some shapes that work, but I'm not sure about how to word a solution or even make a diagram so that it makes sense to anyone. :O

O and I found the error in the "proof".

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