01-16-2021, 10:29 AM
Hi again,
the idea to create wraparound boards from tilings of the plane, by dividing out certain groups acting on the pattern, really caught my interest. I played around a bit, drawing sketches with pen and paper, and figured out that one can very easily put a board on a cube or projected cube this way:
http://manuelhohmann.ddns.net/mhohmann/D.../Cube.html
Also some of the three-player variants can be constructed, but only the once which have boundaries:
http://manuelhohmann.ddns.net/mhohmann/D...riCyl.html
But there is a problem for these ones:
http://manuelhohmann.ddns.net/mhohmann/D...Torus.html
http://manuelhohmann.ddns.net/mhohmann/D...Klein.html
The reason is that one can obtain only particular orbifolds from this construction, and their genus is fixed:
http://xahlee.info/Wallpaper_dir/c5_17Wa...roups.html
Cameron, I also read your slides on general board geometry from the QMUL seminar, which are really instructive and explain very well how boards are implemented. I really like the approach.
the idea to create wraparound boards from tilings of the plane, by dividing out certain groups acting on the pattern, really caught my interest. I played around a bit, drawing sketches with pen and paper, and figured out that one can very easily put a board on a cube or projected cube this way:
http://manuelhohmann.ddns.net/mhohmann/D.../Cube.html
Also some of the three-player variants can be constructed, but only the once which have boundaries:
http://manuelhohmann.ddns.net/mhohmann/D...riCyl.html
But there is a problem for these ones:
http://manuelhohmann.ddns.net/mhohmann/D...Torus.html
http://manuelhohmann.ddns.net/mhohmann/D...Klein.html
The reason is that one can obtain only particular orbifolds from this construction, and their genus is fixed:
http://xahlee.info/Wallpaper_dir/c5_17Wa...roups.html
Cameron, I also read your slides on general board geometry from the QMUL seminar, which are really instructive and explain very well how boards are implemented. I really like the approach.