In an upcoming campaign I'm planning, I would like a combat encounter to take place on a small sphere, with gravity pointing in towards the center. I'd like a sphere about 50' in diameter - something large enough to allow plenty of movement on its surface, but small enough so that players can typically run around it in a few turns.

My problem is setting up the map. My first thought is to purchase a to-scale foam craft sphere, and provide miniatures with small pins so that they stick into the "board." The problem with this, tho, is that I would either need to draw on a geodesic grid by hand or go grid-less, which my group has not done before.

My second thought is to simply use a flat map with "wrapping" edges, so that it acts somewhat sphere-like. The problems with this are that it distorts the distances greatly, and, more importantly, doesn't show the affect that the curvature of the sphere has on line-of-sight. I could get around this by imposing a circular limit to line-of-sight, but I feel it loses much of the effect.

Has anyone attempted to run grid-based combat on a non-flat surface like this? What tools and rules made the combat go smoothly without ignoring important aspects of the unique terrain?
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I would print out a [flattened geodesic sphere](http://sci-toys.com/scitoys/scitoys/mathematics/dome/paper_dome/color_complete.gif) for the minis alongside a printed out and [assembled version of the same](http://sci-toys.com/scitoys/scitoys/mathematics/dome/dome.html#paper_dome), using post-it notes or similar to reference where the minis map to on the sphere. 

For movement, it's triangles instead of squares. Movement along a side is adjacent triangles. I would probably disallow movement across corners, just to make things simpler.
If you are free to alter the dimensions of your planet, you can use any [one of these nice projections](http://en.wikipedia.org/wiki/List_of_map_projections) of a sphere's surface. 

Note that the projections have 24 squares across and top to bottom (15 degrees lat/long each) ie. a 24x24 grid. At 5' per grid square you end up with a circumference of 120' and a 19' radius.

Note that most projections lose a lot of latitude squares near the poles.

Now the trick becomes distance to visual horizon. But again the internet provides a [handy calculator](http://www.neoprogrammics.com/spheres/distance_to_horizon.php).

Using this tool, assuming 6' person gives a surface to horizon of 13'. Making an assumption that double that is hidden. So absolute LOS = 26' = 5 or 6 squares. For fun give anyone in squares 5 and 6 a cover save.