"Kevin Foltinek" <firstname.lastname@example.org> wrote in message news://email@example.com... > "Martin Green" <firstname.lastname@example.org> writes: > > > > Someone once developed a video game that was supposed to be > > > like a 3-d version of Tetris. It was played on a spherical planet > > > that was laid out in a checkerboard. You could rotate the sphere > > > left, right, up, and down, and you always saw this checkerboard > > > pattern in front of you.Topologically, this is impossible on a shpere! > > > (Lines of longitude have to meet SOMEWHERE.) > > > How did the game developers solve this problem??? > > I haven't seen the game, so I'm merely speculating. > > Perhaps the spherical planet is not spherical, but toroidal. (Rather > like the universe in Asteroids, Pac-Man, etc., is a torus.)
Better yet, make it a projective plane. Then you can isometrically embed the entire thing, provided you map each point of the plane to two antipodes of the sphere. Of course, the checkerboard pattern can't continue everywhere in this case, as was required.