Gateway Chess

It turns on the breakdown of two identical Xiang Qi sets and one different one. I imagined that third one to be larger, for reasons that will soon become apparent. You get one of one kind of piece, two each of six kinds, four each of five, five of one, and ten of one. This allows the motif of four each and three simple pieces and two each of their pairwise compounds to be deployed twice over. The threesomes meant a 3d variant - Rook-Bishop-Unicorn and Knight-Sexton-Ninja. The two awkward bits are that there are only ten pieces left over to serve as Pawnlike pieces. That is where the gateway element comes in, so that ten pieces can form a proper barrier.

Setup

Level w

Level x

Level y

Level z

Pieces

	Royally-restricted pieces
	The QUANTUM KING occupies a whole left-to-right row of four cells, and is represented by the large-set General straddling the middle two cells of that row. It moves one step up, down, forward, backward, or along a diagonal combining them. In certain circumstances it must undergo transformation to an Emperor, settling on one of the four cells in the process.

	The EMPEROR moves one step in any of the 26 radial directions. It is unbound, but must be kept out of Check.
	Simple radial linepieces
	The ROOK moves any distance through empty intermediate cells in the 6 orthogonal directions, each of which is the intersection of 2 2d planes and at right angles to the other plane. It is unbound.
	The BISHOP moves any distance through empty intermediate cells in the 12 standard diagonal directions, each of which is a diagonal of a 2d plane and at 45° to the other 2 planes. Each Bishop is bound to half the board.
	The UNICORN moves any distance through empty intermediate cells in the 8 nonstandard diagonal directions, commonly called triagonal, which are all at 35° to all three planes. Each Unicorn is bound to a quarter of the board, which is why there are four of them aside.
	Compound radial linepieces
	The QUEEN is the compound of Rook and Bishop. It inherits the Rook's lack of binding.
	The DUCHESS is the compound of Rook and Unicorn. It inherits the Rook's lack of binding.
	The GOVERNOR is the compound of Bishop and Unicorn. The components' independent bindings make the piece unbound.
	The KNIGHT makes any 2:1:0 leap. The zero smallest coordinate indicates that it always moves within one of the three planes, and the single odd coordinate that it is unbound and colourswitching.
	The SEXTON makes any 2:1:1 leap. The nonzero smallest coordinate indicates that it never moves within one of the three planes, the 2 odd coordinates that it has the Bishop's binding, and the largest coordinate being the sum of the others that it can triangulate. The name puns on its Square of Leap Length being 6.
	The NINJA makes any 2:2:1 leap. The nonzero smallest coordinate indicates that it never moves within one of the three planes, and the single odd coordinate that it is unbound and colourswitching. The name puns on its Square of Leap Length being 9.
	compound 2:m:n leapers
	The CHURCHWARDEN is the compound of Knight and Sexton. Churchwardens start on Wall files e and h, beside the Empress and Emperor respectively. The name means a higher ecclesiastical lay rank than Sexton.
	The SAMURAI is the compound of Knight and Ninja. Samurais start on Wall files b and c, directly above the Empress and Emperor respectively. The name means a Japanese warrior of higher rank than a Ninja.
	The OBERON is the compound of Ninja and Sexton. Oberons start on Frame files a and d, diagonally adjacent to the Empress and Emperor respectively. The name, that of a Shakespeare character, is used here to stand for Oblique baron, from the SOLLS of its components being in a ratio of 2:3 like the radial Baron.
	Forward-oly pieces
	The PAWN is the usual piece from Chess, and has no move in the Unicorn's directions. The board is too complex for me to substitute any of my 3d Pawn substitutes.

Rules

The one-foot-in-the-grave rule applies. This means that each oblique move, and each step on any kind of diagonal, must be in a complete convex block of cells measuring 2x2 for the Bishop and the capturing Pawn, 2x2x2 for the Unicorn, 3x2 for the Knight, 3x2x2 for the Sexton, and 3x3x2 for the Ninja. The same dimensions apply to compound pieces (including Emperors) moving as the relevant component.

It should perhaps also be stressed that no piece may move to, or through the centre of, a cell in the row occupied by a Quantum King, but that a Knight can pass between two such cells.

There is no double-step initial move, En Passant, or Castling.

Transformation takes the place of a normal move. The only circumstances when it can happen are those where it must: when a player has no valid move retaining the Quantum King, or when an enemy piece threatens one or more of the cells that it occupies, or both. It happens in place of a normal move, and the Emperor cannot leave the row altogether until an enemy piece has moved. If a player manages to threaten all four cells occupied by the enemy Quantum King at once, it is Checkmate.

Once a player has an Emperor Check, Checkmate, and Stalemate are as usual.