One thing your game description is still lacking is a rule for how the ranks and files on a face are laid out. In your illustration of an example Territory Face for White, the first rank is on the edge adjacent to the Home Face. When a piece moves to an Open Face, I imagine the ranks and files should be kept consistent. For example, if a face is adjacent to the far rank of one Face, the edge of it that is adjacent should be the first rank of that face. For this to work, Black's Pawns and Spears should go on the last rank of the Territory Faces they begin on. But the question remains whether it can be made to work. Is there some geometric proof that this works, or will someone have to lay out each face with ranks and files on it and check that they all line up?
One thing your game description is still lacking is a rule for how the ranks and files on a face are laid out. In your illustration of an example Territory Face for White, the first rank is on the edge adjacent to the Home Face. When a piece moves to an Open Face, I imagine the ranks and files should be kept consistent. For example, if a face is adjacent to the far rank of one Face, the edge of it that is adjacent should be the first rank of that face. For this to work, Black's Pawns and Spears should go on the last rank of the Territory Faces they begin on. But the question remains whether it can be made to work. Is there some geometric proof that this works, or will someone have to lay out each face with ranks and files on it and check that they all line up?