Vertex Dispenser uses 3d models for its levels - the vertices and polygons of the models are the nodes of territory that you fight over. Quite a variety of levels are possible, but game balance and feel push towards particular kinds of level - moving around on the surface feels best if it's fairly smooth and homogeneous, the colouring rules constrain the degree of vertices, non-triangular faces are very weak, combat works best if the perimeter of a player's territory is in good proportion to the amount of territory (so a player who's winning is vulnerable to attack on more possible fronts). Also, it plays best with around 150-250 vertices - much less and there's no room to build up, much more and the game drags on after one player's already clearly won. And in some vague way, since players impose a lot of structure on the level through their actions in the game, it just kind of feels better for there to be less inherent structure as well.
All this means that the two levels i've found to work best are a plane grid, and a fairly regular sphere (from blender's "icosphere" primitive). Higher-genus surfaces don't work well at all - the torus is acceptable (though not great), and past that you just can't get enough smoothness without having too many vertices.
For some of the campaign levels I've used more intricate models, which work okay for levels with specific goals rather than a full battle to eliminate opposing players. Playtesters have had some difficulty with these though, and even a little with the sphere, so I've made the initial levels use a flat plane, and gradually worked up to other shapes. But then a few weeks back I was showing the game to a few people at the London Indies meetup, and a couple of guys who'd seen it before expressed disappointment at these 2d levels: the unusual shapes of levels are what they'd thought looked cool about it, so in making it more playable I make it less attractive!
I've been working on the final campaign level - originally I had a boss fight against Smestorp, but it turns out that fighting a big enemy with lots of hit points isn't fun in this game so I've had to invent something new - and as well as the above constraints, the design I have for the level requires that a particular subgraph appears, plus a visual effect I want to use looks best if the level is convex. I'd kind of wanted to make a "special" looking level for the ending, but so far I haven't found anything other than a sphere that will work.