Ninepiece Nichtschach

One difference is that I do not treat Crooked, Bent, and Double-Bent pieces interchangeably. A 2d board gives an obvious 2 of each extrapolated from the 2 Straight linepieces. In 3d, however, there are different numbers of pieces of each kind. Only Bent pieces have equal numbers in relation to each of the three Straight pieces. In fact adding Bent pieces squares the 3 to 9 just as adding any kind of non-Straight piece squares the 2 to 4.

As the Bent-piece version of 4LF has no oblique pieces, I decided that this variant should as well. This left equal numbers of 9 kinds of linepiece. I also wanted ranks to be exactly square with even numbers of cells, to make best use of my Stockbroker piece. This gave a choice of 36, which is 4x9, or 64, which is 7x9+1. The latter I rejected as any distribution of 7 of each linepiece would be lopsided. So I settled on a 6x6x6 board with no King, inheriting the rules of 2d Notchess and 3d Nichtschach. This gave the name, which might really be considered a snappy and alliterative shorthand for "Nine-linepiece Fusion Nichtschach".

Setup

level u

level v

level w

level x

level y

level z

Pieces

	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.

	The GRYPHON makes one step as a Bishop, turns 45°, and continues the rest of its move as a Rook.
	The ANCHORITE makes one step as a Rook, turns 45°, and continues the rest of its move as a Bishop.
	The SIMURGH makes one step as a Unicorn, turns 55°, and continues the rest of its move as a Rook.
	The FARRIER makes one step as a Rook, turns 55°, and continues the rest of its move as a Unicorn.
	The CELEBRANT makes one step as a Unicorn, turns 35°, and continues the rest of its move as a Bishop.
	The NAG makes one step as a Bishop, turns 35°, and continues the rest of its move as a Unicorn.

Fusion pieces, same turning angle:
Gryphon+Anchorite=GORGON, Simurgh+Farrier=MECHANIC, Celebrant+Nag=LAYPREACHER.

Fusion pieces, same long-range move:
Rook+Gryphon=REAPER, Rook+Simurgh=HARPY, Gryphon+Simurgh=ROOKSHEATH,
Bishop+Anchorite=HARVESTER, Bishop+Celebrant=EPICURE, Anchorite+Celebrant=BISHOSHEATH,
Unicorn+Farrier=GUNSMITH, Unicorn+Nag=MANTICORE, Farrier+Nag=UNICOSHEATH.

Fusion pieces, same short-range move:
Rook+Anchorite=ANCRESS, Rook+Farrier=FARRIERESS, Anchorite+Farrier=OSTLER,
Bishop+Gryphon=METROPOLITAN, Bishop+Nag=PATRIARCH, Gryphon+Nag=HIPPOGRYPH,
Unicorn+Simurgh=COSMOPOLITAN, Unicorn+Celebrant=GODFATHER, Simurgh+Celebrant=TERMAGANT.

Front rank
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:
(1) noncapturing if orthogonal;
(2) noncapturing if SD and to a file the same distance in/out;
(3) capturing if SD and to a file further in or out;
(4) capturing if ND, including "cutting a corner" with no change in distance in/out.
Note that this makes its moves number:
(a) 3 noncapturing (orthogonal, 1 horizontal and 1 vertical SD) and 6 noncapturing (1 horizontal and 1 vertical SD, 4 ND) from files vb/ve/wc/wd/xc/xd/yb/ye;
(b) 3 noncapturing (orthogonal, 2 horizontal or 2 vertical SD) and 6 noncapturing (2 horizontal or 2 vertical SD, 4 ND) from files vc/vd/wb/we/xb/xe/yc/yd;
(c) 3 noncapturing (orthogonal, 1 horizontal and 1 vertical SD) and 1 noncapturing (ND) from files ua/uf/zu/zf;
(d) 3 noncapturing (orthogonal, 2 horizontal or 2 vertical SD) and 3 noncapturing (2 horizontal or 2 vertical SD, 1 ND) from other files.
In other words, corner files apart it has the same ratio of move types as a Pawn on a 2d board, the leaper files corresponding to the 2d board's edge files. This is one parallel resulting from all ND moves being capturing; the other is that the move crossing through the centre line corresponds to a Pawn move between two equally central files on a even-file square-cell board.

Rules

Stockbrokers reaching the far rank must be promoted to another array piece.

Fusion involves one simple piece making its usual move to a cell occupied by another of the same army. In subsequent moves the combined piece can move as either component. The opposite of Fusion is Fission, in which one component alone makes its usual move to an empty cell and the other component stays where it is. Unpromoted Styockbrokers cannot be involved in Fusion. Pieces can combine only if one of the following applies:
1 both are Straight;
2 both turn by the same angle;
3 both have the same long stage;
4 both ahve the same short stage.

Victory is by capturing all enemy Straight pieces, or all enemy Gryphons Celebrants and Farriers, or all enemy Anchorites Simurghs and Nags (in each case including ones within compounds).

Notes

I considered allowing three-way Fusion, with the constraint that all three components must be pairwise compatible. Even with this constraint, however, I found that I did not have enougb piece names yet. So far I have named only 4 - Rook+Bishop+Unicorn=EMPRESS, Rook+Gryphon+Simurgh=ROOKPLUS, Bishop+Anchorite+Celebrant=BISHOPLUS, Unicorn+Farrier+Nag=UNICOPLUS. As yet 15 have no names - Rook+Bishop+Gryphon, Rook+Bishop+Anchorite, Rook+Unicorn+Simurgh, Rook+Unicorn+Farrier, Bishop+Unicorn+Celebrant, Bishop+Unicorn+Nag, Rook+Gryphon+Anchorite, Rook+Simurgh+Farrier, Bishop+Gryphon+Anchorite, Bishop+Celebrant+Nag, Unicorn+Simurgh+Farrier, Unicorn+Celebrant+Nag, Rook+Anchorite+Farrier, Bishop+Gryphon+Nag, and Unicorn+Simurgh+Celebrant.