3D->2D projection of a cube world?

Hello everyone! I'm working on a strategy game that can be briefly described as chess around the surface of a cube. However, in keeping with the classic board game feel, I would like to maintain a 2D birds-eye view, thus requiring some sort of projection.

I've found ways to capture 3 faces of the cube with triangular* or hexagonal maps, but creating a contiguous looping map is proving quite a challenge. I'm not sure if curving the grid lines is necessary, or if there is a simpler geometric tessellation that can do the trick. Spatial distortion isn't really an issue, so long as all the cells on the map are roughly the same size, there are no points at which more than 3 faces meet, and the same face doesn't wind up adjacent to itself.

Any help or suggested reading material would be highly appreciated.

*(http://api.ning.com/files/c6NeU9ShK6...rtianChess.jpg)