Classic
Classic game of Go with edges and corners.
Torus
Edges wrap around (Like pacman)
Klein Bottle
Edges wrap around like the torus above and below, but flip vertically left and right.
Real Projective Plane
Edges wrap around, but flip horizontally up and down, and flip vertically left and right.
Cylinder
Wrap around like the torus left and right, but the top and bottom are hard edges like classic.
Mobius Strip
Wrap around left and right and flips vertically, but the top and bottom are hard edges like classic.