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An interesting conjugate class
Submitted by mdlazreg on Fri, 01/01/2010 - 11:51.As you know the number of conjugate classes of the cube is 81120.
Unfortunately as far as I know there is no fast way to calculate the optimal distances distribution for a chosen conjugacy class. The only way is to search for the optimal distance of each position one by one. That is what I did for the following conjugacy class:
CE x CC : 1_1_1_1_1_1_1_1_4 x 1_1_1_1_4
which has 495*6*2^3*70*6*3^3 = 269438400 positions and which include the 12 cube generators.
I did this search however only for one orientation which reduced the number to 495*6*70*6 = 1247400 positions. Here is the optimal distribution:
Unfortunately as far as I know there is no fast way to calculate the optimal distances distribution for a chosen conjugacy class. The only way is to search for the optimal distance of each position one by one. That is what I did for the following conjugacy class:
CE x CC : 1_1_1_1_1_1_1_1_4 x 1_1_1_1_4
which has 495*6*2^3*70*6*3^3 = 269438400 positions and which include the 12 cube generators.
I did this search however only for one orientation which reduced the number to 495*6*70*6 = 1247400 positions. Here is the optimal distribution:
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