As someone who’s experimented with hex Go, I don’t recommend it. However a triangular grid is a bit more interesting (although having six liberties to a stone can be just as boring as three)
But some of these modes (like circle and Taurus Go) seem really interesting and it looks like you put a lot of work into this, so I’ll certainly test some out.
Could also do it using a 2d rectangular grid; have to deal with how you display the points/stones on the edges of the grid according to how the edges are glued according to how those points are identified. Compare the Torus with Möbius strip, Klein Bottle and (real) Projective Plane.
Hmmm, something else: On a Nonorientable Surface if you transport a normal vector around (like following the midline of the Möbius strip), the first time it returns to the starting point it points in the opposite direction. So there’s an ambiguity: when you place a stone, which normal vector is pointing at it, or shall one be allowed to play two stones at that point, one on each side? Maybe this is not so easy to do.
Regarding your second point. I suppose you mean tangential vector? It is actually not the case, that the transport of a tangential vector along a closed path (“once around”= a primitive class in \pi_1? You can run twice “around the Moebius-band” without self-intersection!) in a nonorientable manifold gives you the “opposite vector”. For example, in the connected sum of torus and projective plane is non-orientable, and there are certainly paths that do not admit this behaviour. That aside, isn’t the question rather how to “tesselate” the manifold uniformly?
No, the normal vector. There’s a tangent vector to curve but a tangent space at each point on a surface. The normal vector is orthogonal to the tangent space.
I see you have two sizes of Toroidal Go… what are the actual playing sizes? I play 11x11 Toroidal Go on the Little Golem Game Server and have been hoping to start up a bigger Toroidal Go game website, but like you, I’ve had other projects keeping me busy.
