[ygagmvbl] Teleporting higher dimensional chess pieces

Consider one of the orthogonal planes on which a piece lies in 3 dimensional chess.  A piece may have the movement ability to teleport to any empty or enemy-occupied square on that plane (similar to the Emperor piece in 2D tai shogi).  This piece could be considered the 3 dimensional equivalent to a 2D rook.  Teleporting to other diagonal planes, instead of orthogonal, could define other piece types.

Add the ability for a piece to block another piece.  Within a plane one piece can teleport, another piece can create a linear barrier, blocking teleportation beyond that barrier.  Not sure of the details of this.  Does the barrier inducing piece need to be in the same plane as the moving piece?

These ideas can be extended to arbitrary dimensions: in N dimensions, pieces teleport in hyperplanes of N-1 dimensions (as opposed to 1 dimension as previously proposed), and encounter barriers of N-2 dimensions in those hyperplanes.  This even applies to 2 dimensional chess: pieces move along lines, and encounter point-like barriers.