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@siege you could also argue that this is only because 3d and 4d chess are actually the same game as 2d chess just with aesthetic features added.

Or rather if 4d chess is 3d chess in time, then 3d chess is either 2d (standard) chess either in time or on a static physical board but not both.

Continuing the aesthetics vs game affecting function angle, 1d chess could be aesthetic colored line segments jumping around semi-randomly or a sort of linear strongly typed checkers, but is there time???