@chjara don’t remind me of my point mechanics classes

@chjara your grids are going to be probably given by charts, and off the top of my head there’s three charts for a sphere:

• estereographic (covers all but a point, squares squish towards a pole, maybe what they do from your description?)
• solid angles (this is your latitude-longitude business, can cover the entire sphere)
• cylinder projection (this one gives you rectangles near the poles because it ignores the “vertical curvature”)

@chjara That's what DGGS is for. https://en.wikipedia.org/wiki/Discrete_global_grid#Standard_equal-area_hierarchical_grids (via @alcinnz)

@chjara <Nim> stretched cube if you need squares specifically, otherwise icosohedron (grid of triangles, or hexagons with 12 pentagons)

@chjara there is not, at least in euclidean space and without non-uniform tilings

this isn’t a sphere, strictly speaking, but in hyperbolic space you could have an infinite square grid on the surface of a horosphere

@chjara technically a horosphere can be thought of as embedding a euclidean plane into hyperbolic space, but due to the nature of hyperbolic geometry, it looks curved like a ball.

it also exhibits horocyclic properties (a horocycle is to 2D as a horosphere is to 3D) like every point on its surface being tangent to an ideal point