Brookschach

What about symmetric pieces? was my next thought. Could you have a "Stockwazir", "Stockrook", "Stockviceroy" or "Stockunicorn"? The last two were simple cases of matching the forward moves with backward ones, but the first two should have same-rank moves. It struck me that having all same-rank orthogonal moves would be wrong, as some would be like a Rook making a null move. Therefore I decided that they should rather have all same-rank diagonal moves and just the outward/inward same-rank orthogonals, the last being deflected outward again at Frame files in long-range moves. That made nonsense of the names, though, as the pieces would not be an enhanced 3d Wazir and Rook, so I decided to amend them. I came up with Stockbrook - from a tributary of the Brandywine in Lord of the Rings - for the long-range one and Stockfwazir for the short-range one.

The astute among you will already have worked out what the back-formed pieces are. The formal definition is that the Fwazir makes single-step moves as a Wazir between ranks and a Ferz within them, and the Brook makes straight line moves as a Rook between ranks and a Bishop within them. It seemed logical to give the name a more prominent orthogonal piece component as it is an unbound piece with the same number of directions as the orthongonal one, like that piece rotated through 45?. This variant develops the Brook, its rotated forms, and their compounds with each other, which make a fascinating study in piecemaking (sic).

My piece article Man and Beast 12: Alternative Fronts describes a wider range of pieces of the kind used here. I have since added a further article, Man and Beast 15: Strengthened Across the Board, describing the Stockbroker and Stockbrook as one of a wider range of "Stock" pieces.

Setup

Levels v and y

Level w

Level x

Pieces

	The BROOK moves any distance through empty intermediate cells along the forward or backward orthogonal or any same-rank diagonal. It can be considered a Rook rotated 45° around the axis of the file. It is bound to 1 in 2 files. There are 4 Brooks aside, 2 on each binding.
	The SIDEWAYS BROOK moves any distance through empty intermediate cells along the left or right orthogonal or any diagonal changing both rank and level. It can be considered a Rook rotated 45° around the horizontal axis of the rank. It is bound to 1 in 2 intersections of rank and level. There are 4 Sideways Brooks aside, 2 on each binding.
	The LEVEL BROOK is the compound of the Brook and Sideways Brook. It is unbound. There are 4 Level Brooks aside.
	The VERTICAL BROOK moves any distance through empty intermediate cells along the up or down orthogonal or any same-level diagonal. It can be considered a Rook rotated 45° around the vertical axis of the rank. It is bound to 1 in 2 intersections of rank and filestack. There are 4 Vertical Brooks aside, 2 on each binding.
	The FILESTACK BROOK is the compound of the Brook and Vertical Brook. It is unbound. There are 4 Filestack Brooks aside.
	The RANK BROOK is the compound of the Sideways Brook and Vertical Brook. It is unbound. There are 4 Rank Brooks aside.
	The familiar QUEEN is the compound of all three simple Brook pieces. If you don't believe me look at my choice of numbers for the unorthodox pieces. They are based on powers of 2 and their sums. 1 and 6, 2 and 5, and 3 and 4 are each the Rook and Bishop with the same moves swapped, so it is pretty obvious that the sum of any two will be this piece. There is 1 Queen aside.
	The UNICORN of Raumschach moves any distance through empty intermediate cells along the eight triaxial radials, commonly called triagonals. These are the only radials not covered by any of the six types of Brook piece! There are 8 Unicorns aside.
	The EMPRESS moves any distance through empty intermediate cells along any radial. It is the compound of Queen and Unicorn. There is 1 Empress aside.
	The EMPEROR moves one step along any radial and must be kept out of check. There is 1 Emperor aside.
	The pieces covering the front ranks are STOCKBROKERS, an enhanced form of the Broker (which follows rules 1 and 4 and cannot make ND moves at all) but distinct from the Pawnbroker (which follows rules 1 and 4 but extends rule 3 to all SD moves). It moves one step along any of the 9 forward radials with the restriction that the move must be:

Rules

The Emperor may Castle or Cathedral with any piece exactly three steps away on its rank, it being each piece's same-rank move away from that piece. Both pieces move two steps toward each other. Usual restrictions apply.

Stockbrokers reaching the far rank must be promoted. They can become any other capturable array piece, subject to the player never having more than twice the array number of any piece type on the board.

Check. Checkmate, and Stalemate are normal.

Notes