💡📝Joe Joyce wrote on Sat, Feb 4, 2017 09:57 PM UTC:
Geometry was what got me into chess variants, specifically trying to understand 4D for a math course. The connectivity of 4D gives remarkable freedom to the 'normal' chess pieces, and encourages higher-D analogs of the standard pieces, so the "balloon" is a 4D 'bishop'. The 4D 'queen' is often a monster, attacking around a quarter of the 4x4x4x4 board. The knight is the one piece that has a "standard" move in 4D, on square boards. Visualization of moves and counter-moves is something of a problem. (Btw, thanks, you are right about the minimum queen move in hype being 18 squares. Nice catch, sorry 'bout the typo.)
Taking it to hex boards... well, consider that a 4x4x4x4 square board is the smallest one where the knight has freedom/ability to move in all 4 directions from every square on the board. What is the analogous hex board size/shape? To an extent, this depends on the pieces you are using, and their hex footprints. What do you want to achieve?
Geometry was what got me into chess variants, specifically trying to understand 4D for a math course. The connectivity of 4D gives remarkable freedom to the 'normal' chess pieces, and encourages higher-D analogs of the standard pieces, so the "balloon" is a 4D 'bishop'. The 4D 'queen' is often a monster, attacking around a quarter of the 4x4x4x4 board. The knight is the one piece that has a "standard" move in 4D, on square boards. Visualization of moves and counter-moves is something of a problem. (Btw, thanks, you are right about the minimum queen move in hype being 18 squares. Nice catch, sorry 'bout the typo.)
Taking it to hex boards... well, consider that a 4x4x4x4 square board is the smallest one where the knight has freedom/ability to move in all 4 directions from every square on the board. What is the analogous hex board size/shape? To an extent, this depends on the pieces you are using, and their hex footprints. What do you want to achieve?