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   Author  Topic: Cube Through Cube  (Read 2080 times)
ThudnBlunder
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Cube Through Cube  
« on: Sep 22nd, 2008, 4:26pm »		 Quote Quote Modify Modify
I thought I had posted this before but cannot find it. Anyway, it is worth another airing:
 
What is the largest cube that can pass through a unit cube?
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Re: Cube Through Cube  
« Reply #1 on: Sep 22nd, 2008, 4:38pm »		 Quote Quote Modify Modify
Assuming that I correctly understand what you mean by put a cube "through" another cube, (i'm guessing that this is equivalent to finding the largest square contained in the unit cube), I can manage to fit one of side length 32 / 4
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ThudnBlunder
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Re: Cube Through Cube  
« Reply #2 on: Sep 22nd, 2008, 4:49pm »		 Quote Quote Modify Modify
on Sep 22nd, 2008, 4:38pm, 1337b4k4 wrote:
Assuming that I correctly understand what you mean by put a cube "through" another cube, (i'm guessing that this is equivalent to finding the largest square contained in the unit cube), I can manage to fit one of side length 32 / 4

Yep, dunno why I put it in Medium.  Roll Eyes
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Re: Cube Through Cube  
« Reply #3 on: Sep 26th, 2008, 5:19am »		 Quote Quote Modify Modify
What's the largest icosahedron that can be inscribed in the unit octahedron?  Wink
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Grimbal
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Re: Cube Through Cube  
« Reply #4 on: Sep 26th, 2008, 8:46am »		 Quote Quote Modify Modify
In terms of the distance between opposite faces?  Roll Eyes
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Barukh
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Re: Cube Through Cube  
« Reply #5 on: Sep 26th, 2008, 8:48am »		 Quote Quote Modify Modify
on Sep 26th, 2008, 8:46am, Grimbal wrote:
In terms of the distance between opposite faces?  Roll Eyes

In terms of the edge size.
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Grimbal
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Re: Cube Through Cube  
« Reply #6 on: Sep 26th, 2008, 9:10am »		 Quote Quote Modify Modify
According to a small drawing I scribbled on a piece of paper I find:
(3-sqrt(5))/sqrt(2)
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Barukh
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Re: Cube Through Cube  
« Reply #7 on: Sep 26th, 2008, 11:33pm »		 Quote Quote Modify Modify
on Sep 26th, 2008, 9:10am, Grimbal wrote:
According to a small drawing I scribbled on a piece of paper I find:
(3-sqrt(5))/sqrt(2)

Correct! What's the configuration?
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Re: Cube Through Cube  
« Reply #8 on: Sep 27th, 2008, 4:13am »		 Quote Quote Modify Modify
My penultimate post (#4) was a hint for that.
 
8 faces of the icosahedron touch "full-face" the 8 faces of the octahedron.
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