I tried to invert simply the two pins 1 and 12.

Cannot find a solution quickly, please post this string in a comment below to help me improve the solver: [12,6,5,4,3,2,11,7,9,8,10,1]

]]>7,298,706,025,000,999,840 possible iterations versus

479,001,600 pin arrangements. Correct Icosaku solutions being mere fraction of total possible tile arrangements. ]]>

7,298,706,025,000,000,000 as the number of possible tile arrangements is slightly higher than it should be because it treats the four monovalent tiles as trivalent. It is mathematically very difficult to isolate out the rotational neutrality of just 4 of the 20 tiles. 000, 111, 222, 333 if rotated always retain their numerical identities. ]]>