Python Mirrow Coordinates

Question

Is there a easy way to reflect or project 3D Cordinates in Python. For an example: My sphere or cube is divided into 8 pieces. I know the center of it, but i only have the coordinates of 1 pieces, for an example only the coordinatesI ub positive x,y,z direction. a= ( [(x,y,z),(x,y,z)....]). I want the rest of the cube/sphere coordinates.

As an example i have those points marked as blue boxes:

And i want all of the points like here

An example list of my coordinates are:

a=[(0.0, 0.0, 4.0), (0.0, 0.0, 5.0), (0.0, 1.0, 3.0), (0.0, 1.0, 4.0), (0.0, 1.0, 5.0), (0.0, 2.0, 3.0), (0.0, 2.0, 4.0), (0.0, 2.0, 5.0), (0.0, 3.0, 1.0), (0.0, 3.0, 2.0), (0.0, 3.0, 3.0), (0.0, 3.0, 4.0), (0.0, 3.0, 5.0), (0.0, 4.0, 0.0), (0.0, 4.0, 1.0), (0.0, 4.0, 2.0), (0.0, 4.0, 3.0), (0.0, 4.0, 4.0), (0.0, 5.0, 0.0), (0.0, 5.0, 1.0), (0.0, 5.0, 2.0), (0.0, 5.0, 3.0), (1.0, 0.0, 3.0), (1.0, 0.0, 4.0), (1.0, 0.0, 5.0), (1.0, 1.0, 3.0), (1.0, 1.0, 4.0), (1.0, 1.0, 5.0), (1.0, 2.0, 3.0), (1.0, 2.0, 4.0), (1.0, 2.0, 5.0), (1.0, 3.0, 0.0), (1.0, 3.0, 1.0), (1.0, 3.0, 2.0), (1.0, 3.0, 3.0), (1.0, 3.0, 4.0), (1.0, 3.0, 5.0), (1.0, 4.0, 0.0), (1.0, 4.0, 1.0), (1.0, 4.0, 2.0), (1.0, 4.0, 3.0), (1.0, 4.0, 4.0), (1.0, 5.0, 0.0), (1.0, 5.0, 1.0), (1.0, 5.0, 2.0), (1.0, 5.0, 3.0), (2.0, 0.0, 3.0), (2.0, 0.0, 4.0), (2.0, 0.0, 5.0), (2.0, 1.0, 3.0), (2.0, 1.0, 4.0), (2.0, 1.0, 5.0), (2.0, 2.0, 2.0), (2.0, 2.0, 3.0), (2.0, 2.0, 4.0), (2.0, 2.0, 5.0), (2.0, 3.0, 0.0), (2.0, 3.0, 1.0), (2.0, 3.0, 2.0), (2.0, 3.0, 3.0), (2.0, 3.0, 4.0), (2.0, 4.0, 0.0), (2.0, 4.0, 1.0), (2.0, 4.0, 2.0), (2.0, 4.0, 3.0), (2.0, 4.0, 4.0), (2.0, 5.0, 0.0), (2.0, 5.0, 1.0), (2.0, 5.0, 2.0), (3.0, 0.0, 1.0), (3.0, 0.0, 2.0), (3.0, 0.0, 3.0), (3.0, 0.0, 4.0), (3.0, 0.0, 5.0), (3.0, 1.0, 0.0), (3.0, 1.0, 1.0), (3.0, 1.0, 2.0), (3.0, 1.0, 3.0), (3.0, 1.0, 4.0), (3.0, 1.0, 5.0), (3.0, 2.0, 0.0), (3.0, 2.0, 1.0), (3.0, 2.0, 2.0), (3.0, 2.0, 3.0), (3.0, 2.0, 4.0), (3.0, 3.0, 0.0), (3.0, 3.0, 1.0), (3.0, 3.0, 2.0), (3.0, 3.0, 3.0), (3.0, 3.0, 4.0), (3.0, 4.0, 0.0), (3.0, 4.0, 1.0), (3.0, 4.0, 2.0), (3.0, 4.0, 3.0), (3.0, 5.0, 0.0), (3.0, 5.0, 1.0), (4.0, 0.0, 0.0), (4.0, 0.0, 1.0), (4.0, 0.0, 2.0), (4.0, 0.0, 3.0), (4.0, 0.0, 4.0), (4.0, 1.0, 0.0), (4.0, 1.0, 1.0), (4.0, 1.0, 2.0), (4.0, 1.0, 3.0), (4.0, 1.0, 4.0), (4.0, 2.0, 0.0), (4.0, 2.0, 1.0), (4.0, 2.0, 2.0), (4.0, 2.0, 3.0), (4.0, 2.0, 4.0), (4.0, 3.0, 0.0), (4.0, 3.0, 1.0), (4.0, 3.0, 2.0), (4.0, 3.0, 3.0), (4.0, 4.0, 0.0), (4.0, 4.0, 1.0), (4.0, 4.0, 2.0), (5.0, 0.0, 0.0), (5.0, 0.0, 1.0), (5.0, 0.0, 2.0), (5.0, 0.0, 3.0), (5.0, 1.0, 0.0), (5.0, 1.0, 1.0), (5.0, 1.0, 2.0), (5.0, 1.0, 3.0), (5.0, 2.0, 0.0), (5.0, 2.0, 1.0), (5.0, 2.0, 2.0), (5.0, 3.0, 0.0), (5.0, 3.0, 1.0)]

The Center is c = (0,0,0).

With this i only get the 2nd of 8 pieces:

mirrored_points = []
    for point in xyz_pattern:
        mirrored_point = []
        for i in range(3):
            mirrored_point.append(2 * 0 - point[i])
        mirrored_points.append(tuple(mirrored_point))

resulting coordinates, original and mirrowed:

[(0.0, 0.0, 4.0), (0.0, 0.0, 5.0), (0.0, 1.0, 3.0), (0.0, 1.0, 4.0), (0.0, 1.0, 5.0), (0.0, 2.0, 3.0), (0.0, 2.0, 4.0), (0.0, 2.0, 5.0), (0.0, 3.0, 1.0), (0.0, 3.0, 2.0), (0.0, 3.0, 3.0), (0.0, 3.0, 4.0), (0.0, 3.0, 5.0), (0.0, 4.0, 0.0), (0.0, 4.0, 1.0), (0.0, 4.0, 2.0), (0.0, 4.0, 3.0), (0.0, 4.0, 4.0), (0.0, 5.0, 0.0), (0.0, 5.0, 1.0), (0.0, 5.0, 2.0), (0.0, 5.0, 3.0), (1.0, 0.0, 3.0), (1.0, 0.0, 4.0), (1.0, 0.0, 5.0), (1.0, 1.0, 3.0), (1.0, 1.0, 4.0), (1.0, 1.0, 5.0), (1.0, 2.0, 3.0), (1.0, 2.0, 4.0), (1.0, 2.0, 5.0), (1.0, 3.0, 0.0), (1.0, 3.0, 1.0), (1.0, 3.0, 2.0), (1.0, 3.0, 3.0), (1.0, 3.0, 4.0), (1.0, 3.0, 5.0), (1.0, 4.0, 0.0), (1.0, 4.0, 1.0), (1.0, 4.0, 2.0), (1.0, 4.0, 3.0), (1.0, 4.0, 4.0), (1.0, 5.0, 0.0), (1.0, 5.0, 1.0), (1.0, 5.0, 2.0), (1.0, 5.0, 3.0), (2.0, 0.0, 3.0), (2.0, 0.0, 4.0), (2.0, 0.0, 5.0), (2.0, 1.0, 3.0), (2.0, 1.0, 4.0), (2.0, 1.0, 5.0), (2.0, 2.0, 2.0), (2.0, 2.0, 3.0), (2.0, 2.0, 4.0), (2.0, 2.0, 5.0), (2.0, 3.0, 0.0), (2.0, 3.0, 1.0), (2.0, 3.0, 2.0), (2.0, 3.0, 3.0), (2.0, 3.0, 4.0), (2.0, 4.0, 0.0), (2.0, 4.0, 1.0), (2.0, 4.0, 2.0), (2.0, 4.0, 3.0), (2.0, 4.0, 4.0), (2.0, 5.0, 0.0), (2.0, 5.0, 1.0), (2.0, 5.0, 2.0), (3.0, 0.0, 1.0), (3.0, 0.0, 2.0), (3.0, 0.0, 3.0), (3.0, 0.0, 4.0), (3.0, 0.0, 5.0), (3.0, 1.0, 0.0), (3.0, 1.0, 1.0), (3.0, 1.0, 2.0), (3.0, 1.0, 3.0), (3.0, 1.0, 4.0), (3.0, 1.0, 5.0), (3.0, 2.0, 0.0), (3.0, 2.0, 1.0), (3.0, 2.0, 2.0), (3.0, 2.0, 3.0), (3.0, 2.0, 4.0), (3.0, 3.0, 0.0), (3.0, 3.0, 1.0), (3.0, 3.0, 2.0), (3.0, 3.0, 3.0), (3.0, 3.0, 4.0), (3.0, 4.0, 0.0), (3.0, 4.0, 1.0), (3.0, 4.0, 2.0), (3.0, 4.0, 3.0), (3.0, 5.0, 0.0), (3.0, 5.0, 1.0), (4.0, 0.0, 0.0), (4.0, 0.0, 1.0), (4.0, 0.0, 2.0), (4.0, 0.0, 3.0), (4.0, 0.0, 4.0), (4.0, 1.0, 0.0), (4.0, 1.0, 1.0), (4.0, 1.0, 2.0), (4.0, 1.0, 3.0), (4.0, 1.0, 4.0), (4.0, 2.0, 0.0), (4.0, 2.0, 1.0), (4.0, 2.0, 2.0), (4.0, 2.0, 3.0), (4.0, 2.0, 4.0), (4.0, 3.0, 0.0), (4.0, 3.0, 1.0), (4.0, 3.0, 2.0), (4.0, 3.0, 3.0), (4.0, 4.0, 0.0), (4.0, 4.0, 1.0), (4.0, 4.0, 2.0), (5.0, 0.0, 0.0), (5.0, 0.0, 1.0), (5.0, 0.0, 2.0), (5.0, 0.0, 3.0), (5.0, 1.0, 0.0), (5.0, 1.0, 1.0), (5.0, 1.0, 2.0), (5.0, 1.0, 3.0), (5.0, 2.0, 0.0), (5.0, 2.0, 1.0), (5.0, 2.0, 2.0), (5.0, 3.0, 0.0), (5.0, 3.0, 1.0), (0.0, 0.0, -4.0), (0.0, 0.0, -5.0), (0.0, -1.0, -3.0), (0.0, -1.0, -4.0), (0.0, -1.0, -5.0), (0.0, -2.0, -3.0), (0.0, -2.0, -4.0), (0.0, -2.0, -5.0), (0.0, -3.0, -1.0), (0.0, -3.0, -2.0), (0.0, -3.0, -3.0), (0.0, -3.0, -4.0), (0.0, -3.0, -5.0), (0.0, -4.0, 0.0), (0.0, -4.0, -1.0), (0.0, -4.0, -2.0), (0.0, -4.0, -3.0), (0.0, -4.0, -4.0), (0.0, -5.0, 0.0), (0.0, -5.0, -1.0), (0.0, -5.0, -2.0), (0.0, -5.0, -3.0), (-1.0, 0.0, -3.0), (-1.0, 0.0, -4.0), (-1.0, 0.0, -5.0), (-1.0, -1.0, -3.0), (-1.0, -1.0, -4.0), (-1.0, -1.0, -5.0), (-1.0, -2.0, -3.0), (-1.0, -2.0, -4.0), (-1.0, -2.0, -5.0), (-1.0, -3.0, 0.0), (-1.0, -3.0, -1.0), (-1.0, -3.0, -2.0), (-1.0, -3.0, -3.0), (-1.0, -3.0, -4.0), (-1.0, -3.0, -5.0), (-1.0, -4.0, 0.0), (-1.0, -4.0, -1.0), (-1.0, -4.0, -2.0), (-1.0, -4.0, -3.0), (-1.0, -4.0, -4.0), (-1.0, -5.0, 0.0), (-1.0, -5.0, -1.0), (-1.0, -5.0, -2.0), (-1.0, -5.0, -3.0), (-2.0, 0.0, -3.0), (-2.0, 0.0, -4.0), (-2.0, 0.0, -5.0), (-2.0, -1.0, -3.0), (-2.0, -1.0, -4.0), (-2.0, -1.0, -5.0), (-2.0, -2.0, -2.0), (-2.0, -2.0, -3.0), (-2.0, -2.0, -4.0), (-2.0, -2.0, -5.0), (-2.0, -3.0, 0.0), (-2.0, -3.0, -1.0), (-2.0, -3.0, -2.0), (-2.0, -3.0, -3.0), (-2.0, -3.0, -4.0), (-2.0, -4.0, 0.0), (-2.0, -4.0, -1.0), (-2.0, -4.0, -2.0), (-2.0, -4.0, -3.0), (-2.0, -4.0, -4.0), (-2.0, -5.0, 0.0), (-2.0, -5.0, -1.0), (-2.0, -5.0, -2.0), (-3.0, 0.0, -1.0), (-3.0, 0.0, -2.0), (-3.0, 0.0, -3.0), (-3.0, 0.0, -4.0), (-3.0, 0.0, -5.0), (-3.0, -1.0, 0.0), (-3.0, -1.0, -1.0), (-3.0, -1.0, -2.0), (-3.0, -1.0, -3.0), (-3.0, -1.0, -4.0), (-3.0, -1.0, -5.0), (-3.0, -2.0, 0.0), (-3.0, -2.0, -1.0), (-3.0, -2.0, -2.0), (-3.0, -2.0, -3.0), (-3.0, -2.0, -4.0), (-3.0, -3.0, 0.0), (-3.0, -3.0, -1.0), (-3.0, -3.0, -2.0), (-3.0, -3.0, -3.0), (-3.0, -3.0, -4.0), (-3.0, -4.0, 0.0), (-3.0, -4.0, -1.0), (-3.0, -4.0, -2.0), (-3.0, -4.0, -3.0), (-3.0, -5.0, 0.0), (-3.0, -5.0, -1.0), (-4.0, 0.0, 0.0), (-4.0, 0.0, -1.0), (-4.0, 0.0, -2.0), (-4.0, 0.0, -3.0), (-4.0, 0.0, -4.0), (-4.0, -1.0, 0.0), (-4.0, -1.0, -1.0), (-4.0, -1.0, -2.0), (-4.0, -1.0, -3.0), (-4.0, -1.0, -4.0), (-4.0, -2.0, 0.0), (-4.0, -2.0, -1.0), (-4.0, -2.0, -2.0), (-4.0, -2.0, -3.0), (-4.0, -2.0, -4.0), (-4.0, -3.0, 0.0), (-4.0, -3.0, -1.0), (-4.0, -3.0, -2.0), (-4.0, -3.0, -3.0), (-4.0, -4.0, 0.0), (-4.0, -4.0, -1.0), (-4.0, -4.0, -2.0), (-5.0, 0.0, 0.0), (-5.0, 0.0, -1.0), (-5.0, 0.0, -2.0), (-5.0, 0.0, -3.0), (-5.0, -1.0, 0.0), (-5.0, -1.0, -1.0), (-5.0, -1.0, -2.0), (-5.0, -1.0, -3.0), (-5.0, -2.0, 0.0), (-5.0, -2.0, -1.0), (-5.0, -2.0, -2.0), (-5.0, -3.0, 0.0), (-5.0, -3.0, -1.0)]

Example image:

But there are missing 6 of 8 pieces of coordinates, so i think we have to mirrow it to the other axes

Best regards.

EDIT

I used the function of Felix with those points:

list=[(0, 0, 4), (0, 0, 5), (0, 1, 3), (0, 1, 4), (0, 1, 5), (0, 2, 3), (0, 2, 4), (0, 2, 5), (0, 3, 1), (0, 3, 2), (0, 3, 3), (0, 3, 4), (0, 3, 5), (0, 4, 0), (0, 4, 1), (0, 4, 2), (0, 4, 3), (0, 4, 4), (0, 5, 0), (0, 5, 1), (0, 5, 2), (0, 5, 3), (1, 0, 3), (1, 0, 4), (1, 0, 5), (1, 1, 3), (1, 1, 4), (1, 1, 5), (1, 2, 3), (1, 2, 4), (1, 2, 5), (1, 3, 0), (1, 3, 1), (1, 3, 2), (1, 3, 3), (1, 3, 4), (1, 3, 5), (1, 4, 0), (1, 4, 1), (1, 4, 2), (1, 4, 3), (1, 4, 4), (1, 5, 0), (1, 5, 1), (1, 5, 2), (1, 5, 3), (2, 0, 3), (2, 0, 4), (2, 0, 5), (2, 1, 3), (2, 1, 4), (2, 1, 5), (2, 2, 2), (2, 2, 3), (2, 2, 4), (2, 2, 5), (2, 3, 0), (2, 3, 1), (2, 3, 2), (2, 3, 3), (2, 3, 4), (2, 4, 0), (2, 4, 1), (2, 4, 2), (2, 4, 3), (2, 4, 4), (2, 5, 0), (2, 5, 1), (2, 5, 2), (3, 0, 1), (3, 0, 2), (3, 0, 3), (3, 0, 4), (3, 0, 5), (3, 1, 0), (3, 1, 1), (3, 1, 2), (3, 1, 3), (3, 1, 4), (3, 1, 5), (3, 2, 0), (3, 2, 1), (3, 2, 2), (3, 2, 3), (3, 2, 4), (3, 3, 0), (3, 3, 1), (3, 3, 2), (3, 3, 3), (3, 3, 4), (3, 4, 0), (3, 4, 1), (3, 4, 2), (3, 4, 3), (3, 5, 0), (3, 5, 1), (4, 0, 0), (4, 0, 1), (4, 0, 2), (4, 0, 3), (4, 0, 4), (4, 1, 0), (4, 1, 1), (4, 1, 2), (4, 1, 3), (4, 1, 4), (4, 2, 0), (4, 2, 1), (4, 2, 2), (4, 2, 3), (4, 2, 4), (4, 3, 0), (4, 3, 1), (4, 3, 2), (4, 3, 3), (4, 4, 0), (4, 4, 1), (4, 4, 2), (5, 0, 0), (5, 0, 1), (5, 0, 2), (5, 0, 3), (5, 1, 0), (5, 1, 1), (5, 1, 2), (5, 1, 3), (5, 2, 0), (5, 2, 1), (5, 2, 2), (5, 3, 0), (5, 3, 1)]

I get these points:

[(0, 0, 4), (0, 0, -4), (0, 0, 4), (0, 0, -4), (0, 0, 4), (0, 0, -4), (0, 0, 4), (0, 0, -4), (0, 0, 5), (0, 0, -5), (0, 0, 5), (0, 0, -5), (0, 0, 5), (0, 0, -5), (0, 0, 5), (0, 0, -5), (0, 1, 3), (0, 1, -3), (0, -1, 3), (0, -1, -3), (0, 1, 3), (0, 1, -3), (0, -1, 3), (0, -1, -3), (0, 1, 4), (0, 1, -4), (0, -1, 4), (0, -1, -4), (0, 1, 4), (0, 1, -4), (0, -1, 4), (0, -1, -4), (0, 1, 5), (0, 1, -5), (0, -1, 5), (0, -1, -5), (0, 1, 5), (0, 1, -5), (0, -1, 5), (0, -1, -5), (0, 2, 3), (0, 2, -3), (0, -2, 3), (0, -2, -3), (0, 2, 3), (0, 2, -3), (0, -2, 3), (0, -2, -3), (0, 2, 4), (0, 2, -4), (0, -2, 4), (0, -2, -4), (0, 2, 4), (0, 2, -4), (0, -2, 4), (0, -2, -4), (0, 2, 5), (0, 2, -5), (0, -2, 5), (0, -2, -5), (0, 2, 5), (0, 2, -5), (0, -2, 5), (0, -2, -5), (0, 3, 1), (0, 3, -1), (0, -3, 1), (0, -3, -1), (0, 3, 1), (0, 3, -1), (0, -3, 1), (0, -3, -1), (0, 3, 2), (0, 3, -2), (0, -3, 2), (0, -3, -2), (0, 3, 2), (0, 3, -2), (0, -3, 2), (0, -3, -2), (0, 3, 3), (0, 3, -3), (0, -3, 3), (0, -3, -3), (0, 3, 3), (0, 3, -3), (0, -3, 3), (0, -3, -3), (0, 3, 4), (0, 3, -4), (0, -3, 4), (0, -3, -4), (0, 3, 4), (0, 3, -4), (0, -3, 4), (0, -3, -4), (0, 3, 5), (0, 3, -5), (0, -3, 5), (0, -3, -5), (0, 3, 5), (0, 3, -5), (0, -3, 5), (0, -3, -5), (0, 4, 0), (0, 4, 0), (0, -4, 0), (0, -4, 0), (0, 4, 0), (0, 4, 0), (0, -4, 0), (0, -4, 0), (0, 4, 1), (0, 4, -1), (0, -4, 1), (0, -4, -1), (0, 4, 1), (0, 4, -1), (0, -4, 1), (0, -4, -1), (0, 4, 2), (0, 4, -2), (0, -4, 2), (0, -4, -2), (0, 4, 2), (0, 4, -2), (0, -4, 2), (0, -4, -2), (0, 4, 3), (0, 4, -3), (0, -4, 3), (0, -4, -3), (0, 4, 3), (0, 4, -3), (0, -4, 3), (0, -4, -3), (0, 4, 4), (0, 4, -4), (0, -4, 4), (0, -4, -4), (0, 4, 4), (0, 4, -4), (0, -4, 4), (0, -4, -4), (0, 5, 0), (0, 5, 0), (0, -5, 0), (0, -5, 0), (0, 5, 0), (0, 5, 0), (0, -5, 0), (0, -5, 0), (0, 5, 1), (0, 5, -1), (0, -5, 1), (0, -5, -1), (0, 5, 1), (0, 5, -1), (0, -5, 1), (0, -5, -1), (0, 5, 2), (0, 5, -2), (0, -5, 2), (0, -5, -2), (0, 5, 2), (0, 5, -2), (0, -5, 2), (0, -5, -2), 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1, 0), (-5, 1, 0), (-5, -1, 0), (-5, -1, 0), (5, 1, 1), (5, 1, -1), (5, -1, 1), (5, -1, -1), (-5, 1, 1), (-5, 1, -1), (-5, -1, 1), (-5, -1, -1), (5, 1, 2), (5, 1, -2), (5, -1, 2), (5, -1, -2), (-5, 1, 2), (-5, 1, -2), (-5, -1, 2), (-5, -1, -2), (5, 1, 3), (5, 1, -3), (5, -1, 3), (5, -1, -3), (-5, 1, 3), (-5, 1, -3), (-5, -1, 3), (-5, -1, -3), (5, 2, 0), (5, 2, 0), (5, -2, 0), (5, -2, 0), (-5, 2, 0), (-5, 2, 0), (-5, -2, 0), (-5, -2, 0), (5, 2, 1), (5, 2, -1), (5, -2, 1), (5, -2, -1), (-5, 2, 1), (-5, 2, -1), (-5, -2, 1), (-5, -2, -1), (5, 2, 2), (5, 2, -2), (5, -2, 2), (5, -2, -2), (-5, 2, 2), (-5, 2, -2), (-5, -2, 2), (-5, -2, -2), (5, 3, 0), (5, 3, 0), (5, -3, 0), (5, -3, 0), (-5, 3, 0), (-5, 3, 0), (-5, -3, 0), (-5, -3, 0), (5, 3, 1), (5, 3, -1), (5, -3, 1), (5, -3, -1), (-5, 3, 1), (-5, 3, -1), (-5, -3, 1), (-5, -3, -1)]

It seems there are duplicates. Any idea? :)

Answer 1

Ok, still not sure if this is what you want, but check out this function:

In [1]: points = [(25, 296, 4), (27, 296, 5), (24, 296, 6)]

In [2]: center = (24, 294, 1)

In [3]: def mirror_points(points, center):
   ...:     mirrored_points = []
   ...:     for point in points:
   ...:         mirrored_point = []
   ...:         for i in range(3):
   ...:             mirrored_point.append(2 * center[i] - point[i])
   ...:         mirrored_points.append(tuple(mirrored_point))
   ...:     return mirrored_points
   ...:

In [4]: mirror_points(points, center)
Out[4]: [(23, 292, -2), (21, 292, -3), (24, 292, -4)]

The function takes a list of points and returns a list of mirrored points. Each point in the input list is mirrored around the center which produces a single mirrored point.

EDIT

After clarification of the problem:

The task: For each point in the input, calculate all points that are mirrored on any combination of x-, y- and z-planes through the center.

E.g. processing of point (1, 2, 3) around center (0, 0, 0) would lead to the following points:

(-1, 2, 3) # mirrored x-axis
(1, -2, 3) # mirrored y-axis
(1, 2, -3) # mirrored z-axis
(-1, -2, 3) # mirrored x- and y-axis
(1, -2, -3) # mirrored x- and z-axis
(-1, 2, -3) # mirrored y- and z-axis
(-1, -2, -3) # mirrored x-, y- and z-axis

Solution

The following function returns a list of points that contains 8 points for each input point that are mirrored around the center (0, 0, 0):

from itertools import product

def calc_all_point_mirrors(points):
    out = []
    for point in points:
        for factors in product([1, -1], repeat=3): # (1, 1, 1), (1, 1, -1), (1, -1, 1), ..., (-1, -1, -1)
            out.append(tuple(point[i]*factors[i] for i in range(3)))
    return list(set(out))

Example:

>>> calc_all_point_mirrors([(1, 2, 3), (10, 10, 10)])
[(1, 2, 3),
 (1, 2, -3),
 (1, -2, 3),
 (1, -2, -3),
 (-1, 2, 3),
 (-1, 2, -3),
 (-1, -2, 3),
 (-1, -2, -3),
 (10, 10, 10),
 (10, 10, -10),
 (10, -10, 10),
 (10, -10, -10),
 (-10, 10, 10),
 (-10, 10, -10),
 (-10, -10, 10),
 (-10, -10, -10)]