In answer to the question by Dan Hoey, I printed out the unique
antipodal of the 3x3x3 edges [...].It is really quite extraordinary and wonderful. [...]. Without
further ado:
Someone else remarks that it's "got to be all edges flipped in place",
and Jerry Bryan remarks that it is.
*6* *6* 6*6 3*4 *6* *1* *2* *5* 2*2 3*4 *2* *2* *3**1**4* *1**1**1* 3*31*14*4 5*23*42*5 *3**1**4* *6**6**6* *5* *2* 5*5 3*4 *5* *5*
I disagree. Look at the 1-2 edge. If it's "flipped in place", then
since it appears to be fixed, the cube must flip around it. But then
the four 3 faces would be where the 4 faces actually are. No, it's
more complicated than just all-edges-flipped.
"[Q]uite extraordinary and wonderful" it is.
der Mouse
mouse@collatz.mcrcim.mcgill.edu