"Alberto Monteiro" <[EMAIL PROTECTED]> wrote:
>
>The real problem is that "rotation around an axis" is not defined in 3D.
>Maybe we can postulate that each 3D hyperface [and the 3D middle
>cubes] is free to make any rigid body rotation [counting... hmmm...
>6 x 4 positions for each]. But I have no idea if this freedom makes
>the problem too easy or too complex
Two alternate schemes for the 3x3x3x3 were discussed in cube-lovers in the
1980's. I haven't managed to find the message.
I posted the URL for one 3x3x3x3 game earlier
(http://www.superliminal.com/cube.htm); in it, any of the 3x3x3 hyperfaces
can be rotated 26 ways. One nice feature is a "solve" button that shows the
thing spinning itself to a solution.
(On a tangent, I'd love to build a real mechanical 3x3x3 cube with sensors,
stepper motors and a processor so you could scramble the cube then say
"Solve!" and it would solve itself, flopping around on your desk.)
The next step is extending this to other polytopes (hyperpolyhedra):
http://www.cs.utah.edu/~gk/peek/peek.html and
http://plaza.powersurfr.com/jsavard/other/fdiint.htm are interesting
starters.
Or in the other direction, here's a 3x3 infra-cube:
http://www.ggw.org/donorware/3x3cube/
Joshua
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