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My memory is indeed faulty. I was incorrct about the repeated process

which yields the Pons Asinorum. The process I was actually thinking of

does not need a cube rotation to make it have a repeated structure.

(L' R U' D)^3

There is however an interpretation of the standard Process for the Poms, which

can be decomposed into a repeated process by a cube rotation.

Denote by "A", turning by 120 degrees around any diagonal, it doesn't matter

which one, nor in which direction.

(L^2 R^2 A)^3 yields the Pons.