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?
['https://rpg.stackexchange.com/questions/29234', 'https://rpg.stackexchange.com', 'https://rpg.stackexchange.com/users/2161/']
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.
3d movement in D&D is made by dividing the space in cubes. Each cube that's less than 50% filled is a void space, each cube that's not is all filled. If you build a sphere made of cubes you'll get sections similar to a small circle drawn in Paint.

If you get a sphere, sunlight (which rays are parallel) and a transparent sheet with parallel lines you can trace the projection of these lines on the sphere. Rotating the sphere exactly 90° on the 3 axis of the sheet will get you a gridded sheet. The elements of the grid near to the axes will be squared, and the boundaries between those areas will feature triangular elements.  

It's fine, I've explained earlier what they are, corners of a cube. Despite being triangular, they still count as squares.

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As an alternative, this really is a cube, but it looks like a sphere 

[![One practical way to map a square grid to a sphere](https://i.stack.imgur.com/EiHe4.jpg)](https://i.stack.imgur.com/EiHe4.jpg)