I am a physicst and working on titanium dioxide nanoparticles. The geometrical shape of its unit cell is a cuboid (with a=b, not equal to c). It is having one Ti atom at each corner, one Ti atom at body center, two O atoms each at top and bottom faces (at the diagonals) and two O atoms inside cuboid (at the diagonal near body centered Ti). I had calculated the dihedral angles between the nearest neighbouring atoms using a software which is finding the angle by finding the two planes and then calculating normals to the planes and then finding angle between them....(the most obivious method to find dihedral angle)
Now I want to find the possible planes in a unit cell (cuboid) which are making these angles.
There can be so many but i want those that are formed using nearest neighbouring coordinates...
The problem can also be stated as---How to find the possible planes in a geometry having coordinates of all the points at corners of a cuboid , having two coordinates seperated by some distance at the two opposite faces (on the diagonal of the faces), and three coordinates at the body center of cuboid again seperated by some distance (at the diagonal).
How can i find all such possible planes ??
Any suggestion will be highly apprieciated.