I think a move notation system for 3D should best be set up from scratch. It is not only that you need additional atoms for the non-planar moves. You would also need different directional modifiers to select subsets from those. In N dimensions a given atom can have N! 2^N symmetry-equivalent moves, so 48 in 3 dimensions.
The problem with using modifier prefixes in a non-standard way on a Pawn atom is that probably no one would understand what these mean. And that would defeat the purpose. Non-standard Pawn types (other than having a longer range for the initial move on larger boards) are used only rarely, which would both relax the importance of avoiding cumbersome dedicated notations for them, and increase the danger that people would not be familiar with the alternative.
I think a move notation system for 3D should best be set up from scratch. It is not only that you need additional atoms for the non-planar moves. You would also need different directional modifiers to select subsets from those. In N dimensions a given atom can have N! 2^N symmetry-equivalent moves, so 48 in 3 dimensions.
The problem with using modifier prefixes in a non-standard way on a Pawn atom is that probably no one would understand what these mean. And that would defeat the purpose. Non-standard Pawn types (other than having a longer range for the initial move on larger boards) are used only rarely, which would both relax the importance of avoiding cumbersome dedicated notations for them, and increase the danger that people would not be familiar with the alternative.