Well, just really inital thoughts.
Take a cube as an example (like the Rubik's cube 3x3 grid each side so 45 territories in all).
You get several views (different images) of it on a button click to show you each face or rotation.
Bonuses for full face, corners, lines.
Could have objectives of securing corners, middle lines, side, special shapes (like an L shape), something like that.
Only problem is that it's symmetrical so can think of some other polygon if anyone thinks that there is any mileage.
I would like to see a map with different orientation to give it a less 2D feel, so you would really have to think out
what adjoins what (like in this case , the edges adjoin each other).
Anyway just throw this one up and see, need to investigate if it's possible to have multiple maps inside one map
(6 maps for each side combined into one so you can view them).