The Peirce Quincuncial Map can also be seamlessly tiled: [1]. It's a conformal map, meaning that it preserves shapes. But strange things happen at the four cor

The Peirce Quincuncial Map can also be seamlessly tiled: [1]. It's a conformal map, meaning that it preserves shapes. But strange things happen at the four corners of each diamond-shaped tile. If you go around one of those points on the map, you've actually gone around the real point on Earth twice. Also at those points, opposite directions on the map are actually the same direction on the Earth. The technical description of those four points is that they're singularities of the map projection (derivatives of the form d(location on Earth)/d(map coordinate) are undefined). The map looks fine because the four singularities on each tile are in the middle of the ocean. But if you play around with the projection to put any of the singularities inside a landmass, your head will explode. Looking at the AuthaGraph may you linked, it has at least two singularities on each tile. 1. https://en.wikipedia.org/wiki/Peirce_quincuncial_projection#/media/File%3APeirce_quincuncial_projection_SW_20W_tiles.JPG https://en.wikipedia.org/wiki/Peirce_quincuncial_projection#...