Let's invent some very weird pieces

Another idea:

A set of neutral pieces, let's call them Grey. Both Black and White are allowed to move with a grey piece instead of moving with an own piece. Initially, black and white pieces are immune for capture by grey pieces. Once white has taken a grey piece, white pieces are no longer immune for capture by grey pieces. Once black has taken a grey piece, black pieces are no longer immune for capture by grey pieces.

So don't mess with grey pieces unless you see immediate and decisive tactical advantages.

Arcan demon.

An universal leaper piece that can move to any empty place of the board.

For capture a piece from the oponent, such piece must have to the arcan demon in its trajectory of capture.

For example, if a rook has the oponent arcane demon in its trajectory of attack (can capture this), the arcan demon can move to such rook and capture it.

If a opponent knight has your arcane demon in one of the 8 squares where it can move, you can capture such knight.

If your pawn has the opponent arcane demon in its zone of capture (diagonally at front), the opponent arcane demon can capture to your pawn.

Etc,

It seems interesting. About pieces positions, how would each army (of each player) be positioned?

I would bet for have each army (of each player) at ortogonal positions (each army is perpendicular to the other two), but each one separated by the 5 squares between the pawns falanges to a maximal distance of another 5 in trigonal (since these are in perpendicular and not frontal), and crossing dihedrically.

This configuration would give a balanced shape to the game (instead of have one army enfronted versus the other two, these two both diagonally enfronted) and would avoid do captures at the first movement of the game.

What are winged pieces?

As I supposed, the three armies are perpendiculary placed from each other and separated, creating a general dihedral crossed shape (three perpendicular opposite edges of the cube board, each one without the contact with the others, acts like the zones of each different army).

The "flying fucker" is some weird name for a chess piece, but it is not too bad, it makes me remember to some image from the videogames "sacred guns" and "Mark Leung... of course it would not have gained much success either.

I think that a better name for the winged piece is something like "nightmare horse", "pegasus" or "wisp" (the two firsts would be the best possibilities, since do allusion to its knightoid movement).

Anyway I like the concept of a 3D chess for three players, where armies are configured perpendicularly on the three axis instead of frontally (as it is traditionally done), it is a very original idea and, in fact, will give a beatiful appearance to the initial board.

I would like to play this game in a real board.

Regarding the Builder and the Witch.

Since I've got entire sets of Superchess pieces, from wich certain pieces are quite complicate, less known and less used, I've decided to declare that the Superchess pieces Grand Duke and Nymph represent the Builder and Witch respectively.

I've played a couple of games with each of the pieces and conclude that the Witch is perfect on a large board - preferably 10 by 10 - with sufficient long distance pieces. (Added later: castling through the own Witch is allowed, so the Witch is an exception to the rule that no pieces should be between a King and a Rook while castling.)

The Builder however should be changed. Currently, the focus is totally on clustering other pieces around the Builder, and the few pawns near the Builder are already very aggressive from the opening. It would be better to exclude the pawns from his influence, as suggested by some other people before. His movement should at the same time be more agile.

Regarding the Viking:

"Steps (or captures) one square in all 8 directions, or moves or captures like a knight.
1. While going orthogonally, he is not allowed to move to or capture on a square where he sees an enemy piece one orthogonal step away.
2. While going diagonally, he is not allowed to move to or capture on a square where he sees an enemy piece one diagonal step away.
3. While making a knight's move, he is not allowed to move to or capture on a square where he sees an enemy piece a knight's move away."

This way, he's very strong in defending the back ranks, and very weak when he tries to invade the opponent's position. So he is a defender and with him on the board the game is more likely to end in draw or become very slow. I wouldn't have called this piece a Viking if I had realized this.

Fortress piece:
With an unusual bigger size of 2x2 squares (2x2x2 if player 3D), this piece would move like a wazir (one step in ortogonal), but, of course, its steps would ocuppy 2x2 squares, so, it will actually move two steps in each movement.

This bigger size and movement means that this piece is able to capture several pieces at the same time (until 3 or 4 pieces).

Like additional rule, for capture this piece would be needed have such piece in the capture trajectory of at least four pieces (as if it was a kind of fractionary check). If the fortress is inside the attack trajectory of until four opponent pieces or more. this can be capture, otherwise, it can't be captured.

[this, in a 3D chess variant could increase until 6 or even 8 needed pieces]

So, this piece would be very powerful and hard to kill, with a piece value similar to the queen at finite/not too big boards. If played in a very big board or infinite board, its value decays to the value of a knight or slightly higher.

The own king not, but others pieces of your own colour yes.

(Pseudo)Universal leapers variants:

Colorbound universal leaper [shadow]:

An universal leaper that can move and capture to any square of the board, but only if such square is of the colour of where it was placed initially.

Quasicolorbound universal leaper [nightmare]:

An universal leaper that can move and capture to any square of the board, but only if such square is of the contrary colour to where it was placed initially.

Illusionist:

Rook able to leap any number of pieces, bypassing any obstacle in its trajectory, moving or capturing to where it want inside its rook trajectory.

Kraken, elf, etc (3D chess variants):

The elf is an universal leaper able to leap to any square of a set of two coordinates {(m,n,0) or (0,m,n) or (m,0,n)}, ie, it can't move or capture to any square of the 3D board, but can leap to any square of the xy, yz and zx plans that are containing to this piece, as showed at the next image:

Just saw the next pieces developed by Zied Team. Some Animals and some other awesome pieces. Hope Zied will share some pictures here.

The Medusa: A bishop that will turn the piece that captured it unmovable.

The Sun God.

Moves and captures like a queen or Chu Shogi Lion, so really extraordinarily strong.

However, moving with the piece requires the sacrificing of one's own pawn. More precisely, any move with the Sun God must be preceded by taking an aribitrary pawn of the own colour from the board. Once you're out of pawns, the Sun God has become toally useless for you.

It sounds really interesting, but I think it should be possible to sacrificing higher pieces (no pawn, like bishop, rook and knight), that would be useful for prologate the life of the sun queen (although expensively) and specially useful for certain occasions.

I would like to play some chess variant with this piece, may be I will to test it in a standard chess (replacing the queen for a sun queen), but with the previous extra rule added.

A question: how the chu shogi lion moves?

The Chu Shogi Lion can move up to twice as king, potentially capturing two pieces in one turn. In Chu Shogi it is already considered stronger than the queen and here I even want to make the Lion-queen compound.

Seeing your suggestion it could be this way: a player must sacrifice any piece for being allowed to make one move with the Sun God. In most circumstances one would prefer to sacrifice the least expensive piece.

I am always in for a test game. Feel free to bring in any other piece that you invented and would like to test along with it.

the emperor soldier

The Lion+Queen compound occurs in Maka Dai Dai Shogi under the name Buddhist Spirit, as the promted version of the Dark Spirit. The latter is  quite weak piece (like a Ferz, but one of the steps changed in an orthogonal one). But because pieces promote by capturing something, it is not as difficult to promote as Pawns in Chess.

The Buddhist Spirit is furthermore a 'contageous' piece: something capturing a Buddhist Spirit will change into a Buddhist Spirit. (Royal pieces are immune to this.)

The Buddhist Spirit is the strongest piece of Maka Dai Dai Shogi. But I doubt that the Sun God would be worth very strong. Having to sacrifice a piece for every move is just too much. Double captures will be rare, as you have to start them from a square adjacent to your first victim, where it usually is not safe to go. So even if all your moves are captures, you just capture as many pieces as you have to sacrifice. And the chances you can capture anything unprotected without first doing a non-capture are slim. Even requiring a sacrifice only for making a capture would probably to expensive to make the piece very useful.

It might work if you allow the piece to teleport to any empty square on a sacrifice, and then move like a Lion in the same turn. With the additional restriction that you cannot capture a King that way.

It starts with pawns. Play on a big board, with many pawns, sacrifice one or two in order to place the Sun God in a very active position, and the opponent's Sun god has the same disadvantage ... I still would like to try.

One called the MOAB that destroys your opponent's pieces, his board, and his entire hideout 

Perhaps it would work when the Sun God was a Fire Demon that would only burn neighbors at the end of its turn when you sacrifice one of your pieces. The sacrifice would have to be at least the number of pieces you burn. E.g. to burn three pieces, you need to sacrifice a Bishop or Knight, to burn 4 or 5 a Rook, etc.

In a more modest version the burn would be a separate turn (so there is advance warning and an opportunity to capture it before it can burn), and the non-capture move could be that of a Kraken (universal leaper, teleporting to any square).