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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?


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