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.