Tony Paletta wrote on Thu, May 8, 2003 10:01 PM UTC:
In mentioning a three-geometry game, I meant a game which incorporated
piece movements derived from hexagon-tiled, square-tiled and
triangle-tiled chess variants. The board itself would involve one
geometry.
Consider a 12x12 board tiled with equilateral triangles (all have a one
horizontal side, a1 points at W, a2 at B, a3 at W ..., b1 points at B, c1
at W, etc.). Triangle chess movement (as in Dekle's Triangular Chess -
see Pritchard's Encyclopedia of Chess Variants) would be based on the
shapes, standard chess movement on the ranks and files (N leaps 2 ranks, 1
file or 2 files, 1 rank; R slides along rank or along file; B leaps in
1r,1f steps in same direction, etc.) and hexagonal movement would follow a
scheme similar to that in Hexoid Chess (/Rectahex Chesss). A hex-style
three-coloring of the board (a1-blue, a2-yellow, a3-red, a4-blue, ...
b1-yellow, b2-red, b3-blue, b4-yellow, ..., c1-red, c2-blue, c3-yellow,
...) would help a little for the hex movements.
On such a board we could have Standard Knights, Triangular Queens and
Hexagonal Rooks, etc. cheerfully (?) coexisting. Getting the hang of the
game would be a little tough -- but then again, who ever said unified
(playing) field theory would be easy?