Why the Four C's do not Apply!
Draw a line from a1 to h1, and then another from h1 to h8, and from h8 to a8, and connect to the first square a1. You've outlined the 28 edge squares, what I call the Circumference or Circle squares. That space includes the corners, the worst possible squares for any piece on the board excluding pawns, when it comes to where that piece can go from the corner. A bishop has only 7 squares at best when it is locked in the corner, a Knight only 2 and a King 3. Pieces are just generally better in the center of the board - which is fairly the 16 central squares from c3-f3-cf6-c6. Sure, we all know that pieces are better in the center... the Four C's seems to beat a dead horse over that idea. But when the Four C's do not apply is in the event that the side with the 'worse' pieces (worse meaning furthest from the Core) can draw or even win! I believe every chess player has had the experience of having 'bad' pieces yet they actually end up effective pieces. So, is it really better when a piece is nearest the Core squares e4, d4, d5, e5? and worse near the corners?
Since the two armies start at opposite sides of the board, it would be a good idea to just split the Four C's in half! Thus we have a Core, Center, Cage and Circle for both armies! White's Core would thus be e4 and d4, Black's e5 and d5. White's Center would be c4-c3-f3-f4, while Black's would be c5-c6-f6-f5, and so on and so forth. Once your piece INVADES the other side's camp, it will begin to make more sense with the idea of the Four C's., that the nearer the piece is to the Core, and we'll take White's as an example (d4 and e4). Now trace the boxes surrounding those squares and you've got the Center (being c5-c3-f3-f5), around that the Cage, and one layer back is the Circle. Let me demonstrate the difference.
Here the White King is in Black's Circle via e2. The two black pawns indicate the Core, or where White's pieces would be ideally placed, being that those two squares connect to the corners in Black's camp, meaning they connect to both sides of the board left and right. Around those two pawns are Black's Center squares.
Now the White King is in Black's Cage via e3, and the Black pawns highlight the Center squares for Black. These squares are comprised of good and bad. As the White king on e3 is just entering Black's Center, it is technically worse than if it were on e6, being the Center still, yet closer to the enemy king. Thus a piece should try to access forward positions, yet further left or right significantly worsens their activity. (e6 is a great square for a knight, but h6 may prove to be limiting)
Finally there comes the Circle, the outer layer of the board, which in this projection has one subtle difference. Since we are now counting both sides as having a Core, Center, Cage and Circle, we are left with a vacant rank basically at the opposite ends of the boards. That is to say that since Black's Circle is technically extending only to a2 and h2 on White's side, the rank a1-h1 is left with no name, no C! Well, it is actually the other side's Circle. Silly, right? Look at it this way.
An impossible position, but it is meant to show that Black's Circle here begins on the second rank for White, which means that with each developing move for White, the pieces are immediately better. Keeping in mind, of course, that pieces worsen as they approach the Circle... when a piece retreats to its home rank it is effectively on the Circle, and it is also on the circle on the a or h files. But where the piece is isn't as important as where it is going to go.
The two pieces are battling it out. The bishop in this exercise has the dominant position, and the goal is to not allow the knight into the camp, especially not into the Core. So the bishop utilizes the idea of opposition to always stay one step ahead of the knight. If it were white's move then the exercise would be different. What is interesting is that this bishop will always make centralizing moves in order to parry away the knight.
The lines go like this...
A) 1... Nc2 B) 1... Nd1 C) 1... Nf1 D) 1... Ng2
All of which are met by opposition moves by the bishop, trying to keep the Knight from accessing the Core squares. The next diagrams will have Kings on the board, but pay them no attention for now.