We're given a structure, in this case
for a coumpound containing zinc and sulfur
The solid circles are sulfur and the open ones are zinc
And the question is: What's the chemical formula for tis compound?
So what we wanna do is can we count the number
of atoms in some structure like the
eight tubes that are shown
So how many zince atoms do we have
and how many sulfur atoms do we have?
So let's do the easiest one first, the zinc
You notice these, 1, 2, 3 ,4, they're all within the structure
So there are four  zinc atoms
The sulfur atoms,however, are shared, so we can look at
these sulfur atoms first  on the face
and there are six faces
But each sulfur atom is shared with the adjoining
identical structure.  The one above it for example
one below it, one on the sides
We have three sulfur atoms from the faces
We have eight corners.  Now these corner atoms are shared
With seven others, so only one eighth a total of eight
identical structures as we filled out the structure
share these corner atoms so we  have another
one atom from the corners
So that's acounting for the eight corners
we acounted for the faces
and if look at the structure there are no other atoms
So this would say the structure must be
Zinc sulfide, one atom of zinc and one atom of sulfur
