Click on any "General Position Symbol" (one of the circles). The coordinates of that position will appear . Addition to or subtraction from any coordinate (x, y, z) is allowed by translation. (examples: x = x + 1, y = y - 1)
Fractional Crystal Coordinates General Position Diagram orientation of cell
The 0, 0, 0 and 1/2 , 1/2 , 0 above the coordinates for the general positions indicate the centering operation. This is a C centered cell. The C face is the ab face, represented here by the horizontal lines at the top and bottom of the cell. The centering operation takes an object at x, y, x and moves it to 1/2 + x, 1/2 + y, z.
The object at position 1 is reflected through a mirror perpendicular to the b axis at y = 0. The takes an object at x, y, z to x, -y, z. The reflection gives the mirror image, which is represented by the comma. Positions 1 and 2 are at the same x,z position, so the circle is divided to show the two separate positions.
x, y, z
1/2 + x, 1/2 + y, z
x, -y, z
1/2 + x, 1/2 - y, z