If regular octogonal chess would be possible?
Tesselation of regular octogons is impossible in Euclidian geometry. Idea of this game is to show, how octogonal chess would be played, if octogonal tesselation would exist. Use rectangular board and consider diagonally-conected spaces to be connected orthogonally instead (thus, every none-border space have 8 orthogonally-adjecent spaces). This game extends hexagonal chess (in it's most popular sense - with Glinski's pieces) in same way as hexagonal chess extends quadrangular ones (for more clearness, see Betza's Rectahex Chess or my independently invented game with same idea). As well, it extends chess, that would be played on the tesselation, mixing octogons and quadrangles in same they as this tesselation extends square chess.
One may use standart chess setup (with mirror or reverse symmetry). But, since pieces are much stronger here, it seems logical to use larger board with more pieces: rrnnbbkqbbnnrr rrnnbbmabbnnrr pppppppppppppp pppppppppppppp -------------- -------------- -------------- -------------- -------------- -------------- PPPPPPPPPPPPPP PPPPPPPPPPPPPP RRNNBBAMBBNNRR RRNNBBQKBBNNRR A - archebishop (bishop + knight); M - marshal (rook + knight). Well, perhaps this setup is overcrowded, but it's only suggestion, and you may make your one. Setup is not part of the game's idea, it's only the way to make actual playing ok.
Rooks moves along octogonal orthogonals, bishops moves along octogonal diagonals, and knights' moves are respective. To make it clear, i'll describe these moves from viewing board as rectangular (just like in above-mentoided Betza's game hexagonal pieces are described using rectangular board). Roks moves as rectangular queen: x--x--x -x-x-x- --xxx-- xxxRxxx --xxx-- -x-x-x- x--x--x Bishop moves as rectangular knightrider - any number of rectangular knight's leaps in same direction: --x---x-- --------- x--x-x--x --x---x-- ----B---- --x---x-- x--x-x--x --------- --x---x-- Knight moves as rectangular bison - makes (1:3) and (2:3) leaps. As you see, it's octogonal rook's step, followed by octogonal bishop's outward step (without being obstructed, of corse, if you are not playing Xiang-Qi variant), respectively to move of rectangular knight: -xx-xx- x-----x x-----x ---N--- x-----x x-----x -xx-xx- Queen is compound of rook and bishop, of course. King is single-step queen - that is, he can move as rectangular king and rectangular knight: -x-x- xxxxx -xKx- xxxxx -x-x- Pawn can make one rook step forward (not sideways) without capturing and capture with any of four bishop's single forward steps: -c-c- cwwwc --P--
Of course, pawn multistep move and castling rules are not that important, but still they need clarity (you may use different ones though). Pawns may make double step in any of three rook's directions, without turning. In 14x14 setup pawns may make any number of steps towards 7th rank (from owner's perspective), en passant is possible on any crossed square. In 8x8 setup castling is usual (though i don't think it's useful here with such mobile pieces). In 14x14 setup king may make from 2 to 5 steps to castle, while rook lands directly behind him. King may castle with any of four rooks of his rank (of course, to castle with one of corner rooks, rook of 2nd or 13th file must be moved).
This game don't give much new interest for playing, since it's just another one setup with different pieces. But, i hope, it's idea will give material for discussions and inspiration for further variants.
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By Daniil Frolov.
Web page created: 2013-09-04. Web page last updated: 2013-09-20