Every piece keeps its flat-board moves and gains the same moves through the vertical axis. Coordinates read file · rank · level, with the level in Greek — so e2α is the ground floor and e2θ is directly above it at the top.

Pawn always advances a rank, and may hold its level, rise one, or drop one as it goes. It pushes into the cell directly ahead at any of those three heights, and captures one file to either side at any of them — six capture cells. On its first move it may run two cells along any push direction if the path is clear. Reaching the far rank promotes it to a queen. A pawn can never gain height without advancing, and there is no en passant.

Knight makes the classic 2-1 leap, but in any of the three planes rather than only the flat one — eight destinations per plane, twenty-four from an open cell. It still jumps over whatever is in the way.

Bishop slides along any diagonal: two axes at once, or all three at once (a corner-to-corner triagonal).

Rook slides along any one axis, including straight up or down. It also castles with the king, on the ground floor's home rank, under the usual conditions.

Queen does both. King steps one cell to any of its 26 neighbours.