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/']
The line-of-sight benefits are not actually very much, if any. If you've every played wargames with model-based LOS, you're familiar with the excruciating process of eyeballing, using bits of string, and finally arguing over whether being able to draw LOS to a teeny bit of the tip of a sword sticking up above terrain counts as having LOS or not.

Using real LOS, you lose much of the time saved by using a grid. Either go gridless on a sphere and measure everything in real inches, or use a flat, imprecise abstraction with extra LOS limits and movement rules to roughly emulate a spherical surface. Besides which, there's no good tiling of squares onto a sphere that doesn't introduce aberrations in how they connect to each other. To get regularity you have to use a different tile shape, at which point you'd have to make up new rules for adjacency and AOE coverage.
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)