[onqlnqjr] Fairy chess pieces

Let's enumerate a large number of possible fairy chess pieces.

Choose any subset of the 8 square king neighborhood. 5 if avoiding left-right asymmetry.

16 square distance-2 neighborhood.  9 if avoiding asymmetry.  jumping, or intermediate square must be clear, or intermediate square must be clear of enemy, or enemy in intermediate square is captured (like checkers).

Any number of moves along the 8 possible directions. (Or 5)

Each of the above can apply to movement, capture, and stay in one place at destroy a remote piece (artillery).  Cube the possibilities.

Promotion can gain (or lose?) a whole new set of abilities.  Promotion when capture, or when reaching promotion region.

Can an anisotropic directional piece turn, as a move?