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        riddles >> medium >> Cube Through Cube
        
(Message started by: ThudanBlunder on Sep 22nd, 2008, 4:26pm)
Title: Cube Through Cube
Post by ThudanBlunder on Sep 22nd, 2008, 4:26pm
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?
Title: Re: Cube Through Cube
Post by 1337b4k4 on Sep 22nd, 2008, 4:38pm
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 [hide]3http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif2 / 4[/hide]
Title: Re: Cube Through Cube
Post by ThudanBlunder on Sep 22nd, 2008, 4:49pm

on 09/22/08 at 16:38:36, 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 [hide]3http://www.ocf.berkeley.edu/~wwu/YaBBImages/symbols/surd.gif2 / 4[/hide]

Yep, dunno why I put it in Medium.  ::)
Title: Re: Cube Through Cube
Post by Barukh on Sep 26th, 2008, 5:19am
What's the largest icosahedron that can be inscribed in the unit octahedron?  ;)
Title: Re: Cube Through Cube
Post by Grimbal on Sep 26th, 2008, 8:46am
In terms of the distance between opposite faces?  ::)
Title: Re: Cube Through Cube
Post by Barukh on Sep 26th, 2008, 8:48am

on 09/26/08 at 08:46:00, Grimbal wrote:
In terms of the distance between opposite faces?  ::)

In terms of the edge size.
Title: Re: Cube Through Cube
Post by Grimbal on Sep 26th, 2008, 9:10am
According to a small drawing I scribbled on a piece of paper I find:
[hide](3-sqrt(5))/sqrt(2)[/hide]
Title: Re: Cube Through Cube
Post by Barukh on Sep 26th, 2008, 11:33pm

on 09/26/08 at 09:10:02, Grimbal wrote:
According to a small drawing I scribbled on a piece of paper I find:
[hide](3-sqrt(5))/sqrt(2)[/hide]

Correct! What's the configuration?
Title: Re: Cube Through Cube
Post by Grimbal on Sep 27th, 2008, 4:13am
My penultimate post (#4) was a hint for that.

[hide]8 faces of the icosahedron touch "full-face" the 8 faces of the octahedron.[/hide]


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