Three-dimensional chess

First plane of a possible starting position, showing 11 possible pieces

## Pieces

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There are eight likely equivalents to rook, knight, bishop and queen, which have octahedral symmetry.
There are two more likely pieces with pyritohedral and tetrahedral symmetry. (Each with two different orientations.)
The 3D chess variant examined here has 15 named pieces.

Pieces can be bound in two different ways:
Bishop and jester are bound to black or white fields. This shall be called parity.
Envoy and ward can reach only a quarter of all fields, which shall be called red, green, blue and yellow. The term color shall be used for them.
So each field has a parity and a color.   (It is not enough to extend the checkered pattern of the plane into space.)

parity-bound and color-bound

A bishop on a white field can reach only white fields. | A jester on a white field can reach only white fields. | An envoy on a yellow field can reach only yellow fields.
grid with parity and color

6×6×6 chess space | 2×2×2 unit with all eight combinations of parity and color

### Shapes

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The major pieces are represented by polyhedra, whose faces are orthogonal to the direction of capture.   (The design for the pawns is similar.)
In the small images below, the face colors denote direction types, e.g. dark red for axis, blue for plane diagonal, and dark green for space diagonal.

basic

|  |
|  | (0, 0, 1)
cube
rook

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|  | (0, 1, 1)
rhombic dodecahedron
bishop

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|  | (1, 1, 1)
octahedron
envoy

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combinations

|  |
|  | small rhombicuboctahedron
queen

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|  | great rhombicuboctahedron
king

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|  | cuboctahedron
marshal

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jumpers

|  |
|  | (0, 1, 2)
tetrakis hexahedron
knight

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|  | (1, 1, 2)
deltoidal icositetrahedron*
jester

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|  | (1, 2, 2)
triakis octahedron*
archer

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reductions

|  |  |
|  |  | pyritohedra
squire
(half knight)

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|  |  | tetrahedra
ward
(half envoy)

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pawns

The traditional pawn captures along plane diagonals. Another one could capture along space diagonals. One could also combine the two.
To fill the second plane with cheap cover, one may add a weak pawn, that captures only forward.

|  |  |
|  | front
dog |

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|  | plane diagonal
pike |

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|  | space diagonal
lance |

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|  | both diagonals
colonel |

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* The shapes of jester and archer are not Catalan, but integral.

### Moves

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These images indicate the directions of capture as points in a grid.
(In the parity layout the piece is on a white field. In the color layout it is on a yellow field.)

basic

| parity

|  |
rook  | bishop  | envoy
color

|  |
rook  | bishop  | envoy
combinations

| parity

queen / king  | marshal
color

queen / king  | marshal
jumpers

| parity

|  |
knight  | jester  | archer
color

|  |
knight  | jester  | archer
reductions

| parity

|  |  |
squire  | ward
color

|  |  |
squire  | ward
pawns

| parity

|  |  |
dog  | pike  | lance  | colonel
color

|  |  |
dog  | pike  | lance  | colonel

## Space

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An 8×8×8 cube (with 512 fields) would probably be too big. A 6×6×6 cube (with 216 fields) or 6×6×8 cuboid (with 288 fields) seem reasonable.

### Possible starting positions

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Every piece in the first plane, except queen and king, should exist twice. That would be 20 pieces.
The arrangement below is one example how that could look. It is not yet tested.
If the black positions are mirrored, no green pieces of the same type can threaten each other (but octahedra and tetrahedra can).

white polyhedra

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white pawns

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black pawns

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black polyhedra

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