Borderless Goban

A borderless goban is a "double-round" rectangular grid unusual goban, which means, on whichever side you leave the board, you re-enter it at the opposite point. This geometry is also called toroidal, because it corresponds to the surface of a torus (donut shape).
More exactly, a borderless goban can be created by defining the two end points of each row (also, respectively, each column) to be adjacent. Thereby, all points have four neighbours each.
On such a board, any game position constitutes an infinite two-dimensional square crystal structure with period of e. g. 19 points, with the actual board being just an arbitrary 19x19 section of the grid. This 19x19 focus may be shifted by arbitrary steps to get other views onto the (same) game.