(111) plane in BCC

[u_know_who]

Hello, as i mentioned i am studying about crystal structure recently, i am facing another problem. In the book it says that :

(111) plane in BCC does not cut the center atom.

But i do some geometry and i come about that the perpendicular distance from the center of that atom to the (111) plane is 2/3 of the radius of atom. So from my point of view it should cut the atom (since the distance is less than the radius of the atom).

Can anyone help me to find out my mistakes?

[DrDu]

Hello, as i mentioned i am studying about crystal structure recently, i am facing another problem. In the book it says that :

(111) plane in BCC does not cut the center atom.

But i do some geometry and i come about that the perpendicular distance from the center of that atom to the (111) plane is 2/3 of the radius of atom. So from my point of view it should cut the atom (since the distance is less than the radius of the atom).

Can anyone help me to find out my mistakes?
I guess they meant that it doesn't pass through the center of the central atom.

[u_know_who]

So will i take if a plane doesn't pass through the center of the atom we will not count that atom? This thing is not clear in books.