Representing a sphere on a battlemap

Hey there. I'm mapping out a small planetoid for a Pathfinder game and was having some concerns with how to represent a sphere on a square grid. Unfortunately I've got to stick with squares (or my players are likely to complain I think), but I've come up with something that might work, and will probably meet the levels of simplicity that my players will be okay with.

My idea is essentially to take the surface area of the sphere, and get the square root of that, use the root to make two sides of a square, and then divide that square as evenly as I can into 5x5 inciments, saying that each edge of the square loops back to the other side. Probably nowhere near a perfect representation of a sphere, but it could work. What do you folks think? Does anyone have any other easy ways of doing this?

Tycho at Penny Arcade did something similar, using large styrofoam spheres as planetoids flying through the Abyss. I don't have a link handy, but you might want to scour their site to see what you find.

I get the feeling a styrofoam sphere would work better if I wasn't looking to do a square grid. I'd have to draw a grid on for one thing, and I know that wouldn't go well... Actually don't even know if you can fit a square grid perfectly on a sphere.

Another possibility would be to use something like this image (found by searching for '2D sphere' on google images). Duplicate it one so you have two of them, call one the front and the other the back, and leave it at that.

Attachment 42871

That's actually pretty neat, though I get the feeling it would only really work for a sphere of whatever exact sizes I could find in picture form.

Google "map projections" or specifically check out the wikipedia entry. This could work, with some tweaks. It partly depends on what is more important - having each square represent the same physical area, or having specific items on the map appear in the right proportion. You have to distort either size (Mercator) or shape (Peters). Here are some more cool ideas. Good luck!