Jared wrote:
Without spoiling anything, which is more difficult?
Taking everything into account, I think they're about equal. It depends on what aspect of the solve you find the hardest.
The centers of the Pentultimate are the corners on the Icosamate.
The corners of the Pentultimate are the centers on the Icosamate.
The Pentultimate corners on the Icosamate are much easier because they lack orientation but this is somewhat balanced out by the centers on the Pentultimate being harder because they now have orientation.
Worse, overall twist is not maintained for Pentultimate centers / Icosamate corners so this is possible:
Attachment:
icosamate_corner_twist.png [ 17.22 KiB | Viewed 680 times ]
Unless you have a pure sequence for fixing this issue, you need to check for and fix it early in the solve.
Looking at the "difficulty" purely from a number of distinct positions:
Pentultimate positions:
? (20! / 2 * 3^20 / 3 * 12! / 2) / 60
% = 5643573414231758192239391539200000
Icosamate positions:
? (20! / 2 * 12! / 2 * 5^12) / 60
% = 1185469517577945600000000000000000
So the Pentultimate : Icosamate ratio is 4.76 : 1