Rhomboidal Chess

Rhomboidal Chess is a chess variant introduced by Max Koval in 2023. The game is played on a board made of rhombic cells by two players and uses an extended chess set with four additional bishops and pawns per side.

This variant was an attempt to interpret the translation of chess to the rhombic tesselation in an improved way. There are already some variants which incorporate this board, but none of them uses six bishops (and six-colour playing field), although it seems to be a natural case for this tesselation, since if the rook will have four directions, the bishop should also have four, which was never incorporated in other games of this kind.
To decrease the number of bishops for a derivative board tesselation naturally, another variant named Irrational Chess was designed. 

Setup

White: king f2; queen c1; knight b2, g3; rook a1, h4; bishop e1, c2, d2, e2, e3, f4; pawn a2, a3, b4, c4, c5, d6, e5, e6, f6, g5, g6, h6.
Black: king f16; queen c14; knight b12, g16; rook a12, h16; bishop c13, d14, e14, f14, e15, e16; pawn a10, a11, b10, c10, c11, d10, e11, e12, f12, g13, g14, h14.

The way coordinates work is shown below:

Pieces

Rook
The rook moves an arbitrary number of spaces in any orthogonal direction. This is movement in a slightly zig-zag-alike manner along a series of spaces connected by shared sides; every cell is followed by the next one from the previous cells' outer side.

Bishop
Similar to the rook, but in any of four possible diagonal directions (left-down: c6, a4...; left up: c12, a12...; etc). 

Queen
The queen moves like the rook and bishop combined.

King
The king moves like the queen, but only in one cell in any direction. Castling is not specified for this setup.

Knight
The knight's move can be defined as one step in an orthogonal direction, and then one step diagonally in an outward direction. As in standard chess, the knight jumps, and the piece that is jumped over is further not affected by it. That's a 'per defaltam' rule.

Pawn
The pawn's move may look differently depending on which cell it is currently placed; two different types of movement are shown below. Pawn d6 can passively move to c6, e7 and b6, f8 (double step), and attack on d8; pawn e12 can passively move to e13 and attack on c14 and g14. Two step option is available in the initial placement. The promotion zone for white consists of the highest-numbered cells of each column. For black, it is reversed.

Rules

With all the mentioned exceptions, other rules are the same as in orthodox chess. 

Last revised by Max Koval.