Some 3D Pieces that Might be used in 3D chess variants
Of course, every existing two-dimensional piece defines at least one
3D piece. (Two, if you count both the old and new ways of
translating the moves.)
This page is for pieces that are truly 3D.
Pawns
Assuming a Pawn moves straight forward, there are 8 possible squares
where it might be allowed to capture.
From 4e4, these are 4d5, 5d5, 5e5, 5f5, 4f5, 3f5, 3e5, and 3d3.
Several different kinds of 3D Pawn are possible.
- A Flat Pawn on 4e4 (a White Pawn of course) would capture
only on 4d5 or 4f5.
- A Mixed Pawn has 4d5, 4f5, 5e5, and 3e5.
- A Very 3D Pawn has 3d5, 5d5, 3f5, and 5f5.
- An Upright Pawn gets 3d5, 4d5, 5d5, 3f5, 4f5, 5f5.
- A Prone Pawn would therefore be 3d5, 3e5, 3f5, 5d5, 5e5, 5f5!
- A Crazy Pawn would be 3e5 and 5e5.
- Last of all, a Power Pawn would be all 8 possible
squares.
A game with 7 different kinds of pawn would be pretty strange,
wouldn't it? But wait, there's more!
Berolina Pawns
The two-dimensional Berolina Pawn moves the way the standard Pawn
captures, and captures the way the standard Pawn moves.
In 3D, this translates to a one-dimensional capture plus any of the
7 different possibilities of movement (Mixed Pawn, Upright Pawn, and
so on).
The mobility of Berolina Pawns makes them hard to block, so they run
in rather easily to promote (easily compared to the normal Pawns).
In a game with both kinds of Pawn, it might be good to limit the
promotion of Berolina Pawns. (This would also be true in 2D.)
Chinese Pawns
The xiangqi Pawn moves and captures the same way, straight forward,
one-dimensional. Instead of promoting to a powerful piece, it merely
gains the ability to move or capture sideways; and instead of
waiting until it reaches the end of the board, it gets its promotion
as soon as it crosses the midline.
I don't like the idea of having 3 kinds of 3D-Chinese-Pawn with
different promotions (vertical-only, horizontal-only, both).
I don't think that Berolina Chinese Pawns would work.
Sixty-Four Kinds of Pawns
In addition to the fifteen kinds of Pawn defined so far, many others
are possible. Consider that the Alfil in 2D Chess is worth a bit
less than 1.5 Pawns; think of the
Yawn;
probably it would be possible to define a chess variant in which
each player had 64 different kinds of Pawn, and each player had a
completely different set of Pawns, so that no two were alike.
You'd have to be crazy to play such a game, of course, but it's an
interesting idea.
Knights
The basic 3D Knight is (0,1,2). Also possible are (1,1,2) and
(1,2,2), or any combination of the three vectors; seven different
kinds of "Knight".
Of particular interest is the Prone Knight, which would be
the sideways version of the Upright Knight.
Flatland or 3D-Only
Just as you could have "Flatland Pawns" in a 3D game, equally so you
could have "3D-Only" pieces. A 3D-Only Rook moves to any square a 3D
Rook does, except for squares on its starting level.
3D Rides
The "Rose" is a circular Knightrider; the two-dimensional Rose might
start from e1, move to g2, if g2 is empty continue in the same move
to h4, then g6, e7, c6, b4, c2, and return to e1.
Special rule: it is considered unfair for a 3D expert to use the 3D
Rose against a 3D novice. Entertaining, yes, but definitely unfair.
Corkscrew Pieces
A Corkscrew move would be a 3D spiral. For
example, a spiral 3D Rook starting on 1e1 would have, as one of its
many possible moves, the ability to go to 2e2, and if that is empty
to continue as part of the same move to 3f2, 4f1, 5e1, and on.
You could also have a corkscrew circular Knightrider.
It is impossible to represent the corkscrew move on the 2D board.
The same "novice" special rule applies to the Corkscrew.
It would also be possible to have limited 3D pieces, for example, a
variation of the Rook that moves only either on its starting level
or straight up and down; or a variation of the Rook that makes all
the Rook moves *except* on its starting level or straight up+down.
The same for Bishops, of course.
My funny notation wouldn't handle this at all.
Just as the Pawn can only go forward, the Nemesis can only move
towards the enemy King, and the Horace can only go West, there could
be a 3D piece that only descends.
You could have a Rook that rises/descends at half the usual rate,
that is, one-half level per square traversed. From 1a1, it would go
to 1a2, and if empty to 2a3, 2a4, 3a5, 3a6, 4a7, 4a8. This is the
same as a piece that makes a W move followed by an F move, then W
then F and so on; and I think it's described in the crooked-Bishop
page.