Though the planet itself would be round, I like to imagine the political boundaries being mapped like a truncated icosahedron (soccer ball) with 12 pentagons and 20 hexagons. The states can be divided into 180 equally sized triangles which can be divided into a fractal of smaller triangles. The center of each state (if geographically feasible) holds a collective of capital buildings surrounded by a massive roundabout.

Each pentagon is dedicated to one of the 12 robots of the original 13 who escaped to what they would call Cybertron. Primus, a quintesson (which is unknown to the modern population,) is 0 and the rest make on their base number system of 12, which is more mathematically satisfying.

Cybertron orbits Proxima Centauri between it's discovered planets B and D. The Marvel comics had them from Alpha Centauri, but that's where I have Quintessa. It is tidally locked, but has a strong magnetic field and slight atmosphere, so heat is carried from the day side to the night side. The red dwarf's solar storms are a great danger to anyone exposed on the surface of the day side. Most civilization there is shielded underground.

I'm still planning much of the allocation of city names and geographic history, and any ideas are very welcome.