A project for a 4D Chess Variant.

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Angel3D

Jul 8, 2017

I am developing a chess variant of four spatial dimensions, inspired by the videogame "miegakure".

So, I created this thread to receive advice or suggestions from you, the chess variant community, to achieve to create this game; as well as give information about the development of the chess variant.
The base of the game (the board) is already ready, and also some important mechanics.

I just need to decide the location, names, and skills of the large range of pieces that will have; although I also accept receiving criticism or suggestions about finished aspects.

Description of basis:

Board:

Unlike others three-dimensional and fourth-dimensional chess variants, I decided to give strange and unusual mechanics to the game, pieces and board.

One important detail about the board is that it has an irregular shape, unlike the most of boards.

Board will have a size of 8x2x8x3, that can be represented by six common boards: three boards together horizontally, and other three over these three.

The top three boards represent "air", while the lower "land".
Since now these "common boards used to represent the fourth-dimensional board" will be called "layers".

Images of the possible board:
Transverse 2D view (2D cuts):

Transverse 3D view (3D cuts):

(Note that pieces can be placed over the two layers of each of the three 3D cut of the real 4D board)

Types of pieces:

This chess variant, will have different types of pieces, better explained: This chess variant, will have pieces able to go only in land and unable to access the fourth dimension, others able to go in land layer and air layer, others able to move fourth-dimensionally to the other land layers, etc.

This is the classification:

Land pieces:

These only can go through the surface comprised by the x and z axis, ie, only can move horizontally, inside of one land layer (lower board).

Flying pieces:

These can go through the volume comprised by the x, y and z axis, inside one land and one air layers, horizontally and vertically. These CAN NOT move fourth-dimensionally to horizontally adjacent layers.

Transcendental pieces:

These can go through the hypersurface comprised by axis x, z and w. Ie, these can move fourth-dimensionally to horizontally adjacent layers
There is a minor type of transcendental piece, more powerful: trascendental flying pieces or omnidirectional pieces.

These pieces (trascendental flying) can move within the hypervolume comprised within the axis (x, y, z, w axis) hyper-horizontally (through horizontally adjacent boards or layers) and vertically (to the vertically adjacent board, air and land layers), ie, through the totallity of the board.

I thought in the use of classical chess pieces (all these [excepting king] will be land pieces, unable to move vertically or hyper-horizontally).
King will be a transcendental land piece, able to move one step to any direction inside the hypersurface comprised by the x, z and w axis.

There is also some planned pieces, mainly a piece called "pantheon" (that is basically a 4D rook, but unable to move vertically, ie, a trascendental land piece that can move orthogonally through the hypersurface comprished by x, z and w axis).

Presenting guardians of the fourth dimension:

I created a set of three pieces called "guardians of fourth dimension". All these are transcendental flying pieces, so, these can move hyper-horizontally and vertically.

These are the pieces:

Tesseract guardian:

this piece would have a tesseract shadow shape or, in its defect, a cube shape. Tesseract guardian can move one step orthogonally (like rook) or diagonally (like bishop), but only one step.
3D representation of its movement on a 5x5x5x5 board:

Hyper-diamond guardian:

this piece would have a orthoplex (16-cell) shadow shape or, in its defect, a crossed cube or octahedron shape. Hyper-diamond guardian can move one step diagonally (like bishop) or trigonally (through cubic diagonals, ridges of the hypercube), but only one step.
3D representation of its movement on a 5x5x5x5 board:

Octocube guardian:

this piece would have a octoplex (24-cell) shadow shape or, in its defect, a octahedron or cuboctahedron shape. Octocube guardian can move one step trigonally (through cubic diagonals, ridges of the hypercube) or quadragonally (through hypercubic diagonals, peaks of the hypercube) but only one step.
3D representation of its movement on a 5x5x5x5 board:

2D representation of the movement of the three previous fourth-dimensional guardians, in 5x5x5x5 boards:

I will still updating this topic for give information about the development of the game, but it is possible to follow the development of the chess variant more nearly on reddit (https://www.reddit.com/r/chessvariants/comments/6lmnbb/a_project_for_a_4d_chess_variant/)

davidkaufmann