Three-dimensional chess



Pieces
There are eight likely equivalents to rook, knight, bishop and queen, which have. 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.)

Shapes
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.

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

Moves
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.)

Space
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
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).