Flipped-return Nichtschach

My first thought was the stronger pieces moving as Rook, Bishop, Knight, and their compounds and switching with weaker pieces. Shogi's back rank would represent their FIDE positional counterparts promoted, and the weaker versions unpromoted. Shogi's middle rank would represent knighted pieces promoted, and their weaker versions (not themselves, note) unpromoted. The King would represent the Queen (so a Kingless variant) and the Gold its weaker counterpart - swapping those two corresponding to the more usual flipping.

As the only satisfactory weaker Knight counterpart seemed to be the Crab, and I wanted different weak pieces for each subvariant, I dropped the Knight. That left five FIDE piece types - which meant a lot of the Shogi set going unused. Next I asked: "Well what radial piece do I sometimes substitute for a Knight?" The answer was the similarly equine Unicorn. Thus this came to be a 3d variant, and I chose to use a 6x6x6 board with 4 identical Shogi sets. That gave files for 4 each of the 6 simple piece types, and 2 each of the 6 compound piece types. The second rank was filled with 4 lots of the Shogi front rank.

The perfectly cubic board also influenced the name as the ending -schach is my marker for such a board, inspired by Raumschach. My first thought was Doppelgängerschach. Only when I posted the page and it failed to turn up on the lists did I think to check whether the Doppelgänger had any existing meaning in Chess variants. It had and I guessed that the similarity to the names of existing variants was the reason for it not appearing.

Deciding to rethink it, I noticed a certain similarity to my earlier Nichtschach. The use of 4 each of 6 types of simple piece and 2 each of 6 kinds of compound piece is one similarity; the lack of Check/Checkmate/Stalemate is the other. So I settled on naming the general idea as a particular form of Nichtschach, with the prefixes added to the plain Nichtschach.

I devised several subvariants, but all with the same long-range pieces. Originally the four main subvariants were ELEFANTNICHTSCHACH (based on historic predecessors real and notional), GENERALNICHTSCHACH (hard G and extrapolating from Shogi's own generals), SCHWEINNICHTSCHACH (this page being first posted in the Year of the Pig), and RAJNICHTSCHACH. Since then I have added others but only one, PASCHANICHTSCHACH, do I consider a main one of the same kind. This one was delayed until I was happy with the names for the short-range pieces. I have also added SPRINGERNICHTSCHACH, reintroducing the Knight, to the main variants as its array is easy to do now that I have established images for its pieces.

Setup

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Elefantnichtschach

Level u - mirror for level z

Level v - mirror for level y

Level w - mirror for level x

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Generalnichtschach

Level u - mirror for level z

Level v - mirror for level y

Level w - mirror for level x

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Schweinnichtschach

Level u - mirror for level z

Level v - mirror for level y

Level w - mirror for level x

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Rajnichtschach

Level u - mirror for level z

Level v - mirror for level y

Level w - mirror for level x

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Paschanichtschach

Level u - mirror for level z

Level v - mirror for level y

Level w - mirror for level x

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Springernichtschach

Level u - mirror for level z

Level v - mirror for level y

Level w - mirror for level x

Pieces

Front-rank pieces and their promoted forms are common to all subvariants.

The STOCKPOINT moves one step forward along a Rook or Bishop line, but always one keeping it on a file the same distance in or out. These always add up to three possible moves. Until promoted or captured a Stockpoint always remains on either files wc/wd/xc/xd, files vb/vc/vd/ve/wb/we/xb/xe/yb/yc/yd/ye, or levels u and z and filestacks a and f. They cannot "cut corners" along a Unicorn line (see below) or move within a rank. As Shogi is so strong an influence I chose them as more Shogi-analogous than the divergent Stockbrokers. They are represented by unpromoted Points.

Long-range pieces are common to all subvariants. They all move any distance through empty intervening cells. They are represented by Shogi's Kings and promoted pieces.

	The ROOK, the BISHOP, and their compound the QUEEN are FIDE pieces extended from one plane to three with the resulting increase in directions. Each Bishop remains bound to half the board.
	The UNICORN of Raumschach differs from these pieces in moving along, and only along, the root-3 diagonals that do not exist between square cells in 2d. It is bound to a quarter of the board and specifically to a quarter of both Bishop bindings, rather than half of just one.
	The DUCHESS and GOVERNOR are the Unicorn's compounds with the Rook and Bishop respectively. Both are unbound.

Short-range pieces are represented by Shogi's Golds and unpromoted pieces.

Elefantnichtschach short-range pieces move exactly two cells in their long-range counterparts' directions. They cannot be blocked by a piece halfway, as this is extreme enough of strength and weakness with the pieces having such small bindings.

	The DABBABA, the ELEPHANT, and their compound the ALIBABA will be familiar to readers of these pages. The Elephant is known to be the piece replaced by the Bishop during the history of Chess in Europe. The Dabbaba is thought by some to have been replaced by the Rook in India a millennium earlier. Each Dabbaba or Alibaba is bound to the intersection of a Bishop and Unicorn binding, comprising a quarter of the former and half the latter. Each Elephant (represented physically by its Shogi replacement!) is bound to half a Dabbaba binding.
	The EUNUCH moves two cells in the Unicorn's directions. The name is a deliberate soundalike for Unicorn, but starting with the E of Elephant. It also conveys the weakness of the piece, which is bound to a quarter of a Dabbaba binding - again a quarter of both Elephant bindings therein rather than half of just one.
	The DYBBUK and ELK are the Eunuch's compounds with the Dabbaba and Elephant respectively. Both have the Dabbaba's binding. The names, meaning a demon of Jewish mythology and a large ungulate, are modelled on Alibaba's combining of component names.

Generalnichtschach substitutes pieces moving only one cell instead of two, but in all 9 forward directions as well as those of their long-range counterparts. They cover ground slower than Elefantnichtschach pieces but can reach any cell of the board.

	The SUNGENERAL moves in 13 directions. It combines the enhancements converting a Wazir to a Goldgeneral and to a Brassgeneral, and is named as the strongest of the "yellow" generals and in allusion to the alchemical link between gold and the Sun.
	The MOONGENERAL moves in 16 directions. It combines the enhancements converting a Ferz to a Silvergeneral (the suggested physical representation!) and to a Steelgeneral, and is named as the strongest of the "whitish" generals and in allusion to the alchemical link between silver and the Moon.
	The SKYGENERAL moves in 21 directions. It is the corresponding enhancement of a Prince, and is named after the expanse in which both Sun and Moon are seen.
	The COASTGENERAL moves in 12 directions. It combines the enhancements converting a Viceroy (1-step piece in the Unicorn's direction) to an Azuregeneral and to a Jadegeneral, and is named for where the blue of the sea meets the green of the land.
	The FORESTGENERAL moves in 17 directions. It is the corresponding enhancement of a Duke, and is so named because the growth of the forest is an effect of the Sun on the area one side of the coast.
	The SEAGENERAL moves in 20 directions. It is the corresponding enhancement of a Baron, and is so named because the tides of the sea are an effect of the Moon on the area the other side of the coast.

Schweinnichtschach is intermediate between the two previously-mentioned subvariants. Its short-range pieces move one cell in all their long-range counterparts' directions, or two cells in just those pieces' forward directions. They share their long-range counterparts' bindings or lack thereof. Their names are explained in my piece article Man and Beast 11: Long-Nosed Generals.

	The SOW moves like a Wazir or Dabchick (forward Dabbaba).
	The BOAR moves like a Ferz or Tusk (forward Elephant).
	The HOOD is the compound of Sow and Boar, but can also be seen as that of Prince and Thief (forward Alibaba).
	The PIGLET moves like a Viceroy or Key (forward Eunuch).
	The FIEND is the compound of Sow and Piglet, but can also be seen as that of Duke and Imp (forward Dybbuk).
	The LAIRD is the compound of Boar and Piglet, but can also be seen as that of Baron and Antler (forward Elk).

Rajnichtschach enhances Elefantnichtschach by adding a move one cell in their forward directions. The Memsahib is bound to one in four files, but the rest share their long-range counterparts' bindings or lack thereof. Their names are explained in my piece article Man and Beast 11: Long-Nosed Generals.

	The MEMSAHIB moves like a Dabbaba or Point (forward Wazir).
	The SAHIB moves like a Elephant or Cross (forward Ferz).
	The ALADDIN is the compound of Memsahib and Sahib, but can also be seen as that of Alibaba and Princeling (forward Prince).
	The NABOB moves like a Eunuch or Saltire (forward Viceroy).
	The IDOLATOR is the compound of Memsahib and Nabob, but can also be seen as that of Dybbuk and Count (forward Duke).
	The FAWN is the compound of Sahib and Nabob, but can also be seen as that of Elk and Heir (forward Baron).

Paschanichtschach enhances Elefantnichtschach by adding a move one cell in all directions. They share their long-range counterparts' bindings or lack thereof. Their names are explained in my piece article Man and Beast 06: The Heavy Brigade.

	The WAZBABA moves like a Wazir or Dabbaba.
	The FEARFUL moves like a Ferz or Elephant.
	The PASHA is the compound of Wazbaba and Fearful, but can also be seen as that of Prince and Alibaba.
	The VINNOCK moves like a Viceroy or Eunuch.
	The KHAN is the compound of Wazbaba and Vinnock, but can also be seen as that of Duke and Dybbuk.
	The IMAM is the compound of Fearful and Vinnock, but can also be seen as that of Baron and Elk.

Springernichtschach short-range pieces are the oblique ones to the second perimeter (so the Knight, called Springer in German, gets in after all). They are in fact the ones of Nichtschach itself, albeit in different array positions. This makes for quite a concentration of power here as they keep returning. They are;
NINJA (2:1:0, with an integer move length)
SEXTON (2:1:1, with the Bishop's binding and its name the title of a minor church official)
OBERON (Ninja+Sexton)
KNIGHT (2:1:0, represented here by its Shogi replacement!)
SAMURAI (Ninja+Knight)
CHURCHWARDEN (Sexton+Knight).

A slightly different approach is Bärnichtschach, in which the standard pieces' counterparts are their odd-only counterparts, which share their bindings or lack thereof. These pieces have various kinds, described in my piece article Man and Beast 06: The Heavy Brigade, but I envisage using the stepping ones (blockable anywhere en route).
The PANDA (odd-only Rook) always changes both Bishop and Unicorn bindings. The name is well-established despite not currently being in the Piececlopedia.
The BEAR (odd-only Bishop) always changes Unicorn binding but never Bishop binding. The name is my analogy on the basis of all-black and all-white bears (the traditional colours of Bishop bindings) corresponding to the black-and-white giant panda.
The HARLEQUIN (Panda+Bear) always changes Unicorn binding. Each "other" Unicorn binding corresponds to all Bear moves in a given plane and all Panda moves at right angles to that plane. The name is from the idea of moving between four Unicorn (or in 2d four Dabbaba) "colours" as well as suggesting the word Queen of which it is the odd-only form.
The RACCOON (odd-only Unicorn) always changes Dabbaba binding but never Unicorn binding. The name is after a relative of the obscure red panda (which is unsurprisingly smaller than the giant one!)
The PANTALOON and BALLOON are the Raccoon's compounds with the Panda and Bear (such as Kipling's Baloo) respectively. Pantaloon is a character alongside Harlequin whose name combines the component pieces, and Balloon the most similar word replacing the P of Pandas with the B of Bear.

Hummernichtschach (hummer being German for lobster) short-range pieces differ from Schweinnichtschach ones in that in the forward directions they have only the two-cell move. They still have their counterparts' bindings.
The SNAIL moves as a Wazir except in the forward direction, in which it moves as a Dabbaba.
The LOBSTER moves as a Ferz except in forward directions, in which it moves as an Elephant.
The TRILOBITE moves as a Snail or a Lobster.
The SHRIMP moves as a Viceroy except in forward directions, in which it moves as a Eunuch.
The PRAWN moves as a Snail or a Shrimp.
The OCTOPUS moves as a Lobster or a Shrimp.

Rules

Stockpoints have no initial double-step move and no En Passant. With no royally-restricted piece there is no Castling.

Stockpoints reaching the far rank are promoted to Stockfwazirs.

A player capturing an enemy piece can reintroduce it as its counterpart in place of a normal move. A captured Stockpoint returns as a Stockfwazir and vice versa, in the latter case within the capturing player's camp.

In variants with only radial pieces, a player must retain at least two pieces moving in each of the 26 directions. The smallest number of pieces that can do so is a Queen or its counterpart, a Duchess or its counterpart, and a Governor or its counterpart, although it can also be done with a larger number of pieces with fewer directions each. Springernichtschach requires retaining two pieces with a Rook or Ninja move, two with a Bishop or Sexton move, and two with a Unicorn or Knight move. A player ceasing to have the required combination loses.

Notes

My definition of the Lobster in 3d is perhaps questionable. This is the problem of move definitions giving identical results in 2d but different ones in 3d. The definition that I am taking is that the Lobster moves along diagonals, 2 steps on the forward ones and 1 on the rest - including same-rank ones in 3d.