To help in seeing piece movement, considering the individual orthogonal steps that make up a move often helps.(In the above figure, white promotes at 44 and black at 11.) Notes Pawns do not have an initial two-step (and hence no en passant), and promote upon reaching their forward-most row. The object is to checkmate the opposing king. It captures one square diagonally forward-sideways that is, it makes one step in one of the two forward directions, and one step in one of the four non-forward directions (it never actually lands in the intermediate cell). The pawn moves without capturing one square in either of the two forward directions ("big" or "little").
4 D CHESS PLUS
That is, it moves 2 squares in one direction plus 1 square in a another direction (not opposite the first), and no squares in either of the last two directions. The knight moves as a FIDE knight in any of the (axis-aligned) planes that it occupies. The king steps one cell in any direction.
The bishop slides along diagonals or quadragonals. The rook slides along orthogonals or triagonals. In order to have piece strength relatively balanced, and to avoid having at least 8 quadragonal sliders per player, we will not use these elemental pieces, but rather combinations of them. In 4D, the orthogonal slider is rather weak, and the quadragonal slider is restricted to one of eight "bindings". Geometrically, that corresponds to moving through cells' cubic faces, square faces, edges, and vertices, respectively. They are referred to as orthogonal, diagonal, triagonal, and quadragonal sliders, respectively. In 4D chess, it is natural to have four basic sliders: these pieces change one, two, three, or all four of their coordinates by the same absolute value each move. Other setups have been playtested, and this is the current favorite, but maybe a better one exists. In visualizing moves, it is sometimes helpful to imagine stacking the small boards on top of each other, into a line of 3D boards: all valid moves in these 3D boards are valid in TessChess. In this layout, the 4 dimensions can be called "small left/right", "small forward/backward", "big left/right", and "big forward/backward" (from a given player's perspective anyway). As is standard for 4D games, the board will be laid out as a 4x4 array of 4x4 chessboards. TessChess is played in a 4x4x4x4 hypercube. I would like to thank Arlona Schulz for her help in inventing the game, and Joe Joyce for helping to playtest starting arrays and checkmate options. I hope TessChess and its variants help to fill this gap.
The former has some complicated rules, and the latter is perhaps not very chesslike. I am aware only of two 4D variants that have pieces moving symmetrically: Chesseract and Timeline (both can be found in the 4D category of this site). That game, and several other 4D (and even many 3D) variants lack the symmetry that is present in 2D chess. The idea for this game came out of dissatisfaction with V.R. This page is written by the game's inventor, Ben Reiniger. Check out Opulent Chess, our featured variant for July, 2023.
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