The motivation for this thread comes from physics, but I'm posting it in the maths section as the question is more of a mathematical one and less concerned with the underlying physics. In cosmology, they often talk about closed universes with positive curvature, or non-Euclidean elliptic geometry. The balloon analogy is often used as well. Think of a spherically shaped universe. Now, imagine an infinite grid on an infinite plane. An infinite grid consists of tessellating squares. Each square is surrounded by eight other squares. Imagine trying to draw a grid on the surface of a sphere. You want the entire surface of the sphere to be covered by the squares of the grid. You want each square to be surrounded by eight other squares. You can use convex quadrilaterals instead of squares too. The important issue is to obtain a continuous symmetrical grid. Is this mathematically possible?