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An analysis of the corner and edge orientations of the 3x3x3 cube

An analysis of the corner and edge permutations of the 3x3x3 cube has already been done by Bruce Norskog. His results for the quarter-turn metric are:
Distance       Positions    
--------       ---------    
 0q                    1    
 1q                   12    
 2q                  114    
 3q                1,068    
 4q               10,011    
 5q               93,840   
 6q              877,956   
 7q            8,197,896   
 8q           76,405,543   
 9q          710,142,108   
10q        6,565,779,580   
11q       59,762,006,092   
12q      506,821,901,799