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Don't know why I had the strange urge to make this image.
The 720 ways to join the opposite corners of a cube by going through every
vertex. (Yes, there are symetries and, yes, there are lines crossing within
some permutations... still have to find an elegant way to solve these.)
(Pity the image compresses so badly, I really had to squeeze it)
Povingly,
Philippe
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Attachments:
Download '720cubewalks.png' (61 KB)
Preview of image '720cubewalks.png'
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Unusual. Cool.
I was going to ask if you are allowed to go through the center of the
cube to an opposite corner, but I should realize that 720 is 6!, so
yes. :)
Now find the number such that a path can't intersect itself. ;)
--
David Fontaine <dav### [at] faricy net> ICQ 55354965
My raytracing gallery: http://davidf.faricy.net/
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On Fri, 9 Nov 2001 00:15:40 +0100, Philippe Debar wrote:
>Don't know why I had the strange urge to make this image.
>
>The 720 ways to join the opposite corners of a cube by going through every
>vertex. (Yes, there are symetries and, yes, there are lines crossing within
>some permutations... still have to find an elegant way to solve these.)
Noodeles of the Borg:-)
--
Cheers
Steve email mailto:ste### [at] zeroppsuklinuxnet
%HAV-A-NICEDAY Error not enough coffee 0 pps.
web http://www.zeropps.uklinux.net/
or http://start.at/zero-pps
12:52pm up 32 days, 4:34, 1 user, load average: 1.00, 1.00, 1.00
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"David Fontaine" <dav### [at] faricynet> wrote in message
news:3BEB5A0F.6F34925B@faricy.net...
> Unusual. Cool.
;-)
> I was going to ask if you are allowed to go through the center of the
> cube to an opposite corner, but I should realize that 720 is 6!, so
> yes. :)
>
> Now find the number such that a path can't intersect itself. ;)
I count 486 of them. (Actually my pov-code counts them, I just repeat
dumbly... Humans don't do mistake, they merely do whatever the computers
tell them.)
I currently believe that there are 81 different paths, the others are just
rotations/symetries of these.
Povingly,
Philippe
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Philippe Debar wrote:
>
> ;-)
>
> > Now find the number such that a path can't intersect itself. ;)
>
> I count 486 of them. (Actually my pov-code counts them, I just repeat
> dumbly... Humans don't do mistake, they merely do whatever the computers
> tell them.)
>
> I currently believe that there are 81 different paths, the others are just
> rotations/symetries of these.
486 divided by three rotations, two reflections, that seems to be right.
I think there's 72 if you are confined to the surface of the cube, no
going to the opposite corner.
--
David Fontaine <dav### [at] faricynet> ICQ 55354965
My raytracing gallery: http://davidf.faricy.net/
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