Counting Stamps

The way $Li_2$ displaces a $Fe$ in the lattice of $FeS_2$ puts the validity of oxidation numbers into question.  The formula $FeS_2$ is arrived at after the considering the number of neighbors the basic unit member of the lattice has. In this case, the basic unit member containing $Fe$ has six $S$ around it, two of these are connected to another unit member.  Six $S$ are shared by three other unit members.  This make on average, two $S$ for each $Fe$, and thus the formula $FeS_2$.  When one $Fe$ is replaced, half of the two $Fe$ out of six in total is removed.  From the diagram repeated below, $Fe$'s oxidation state is reduced by one, from $+6$ to $+5$.

But the formula,

$Li_2FeS_2$

indicates that the oxidation state of $Fe$ has reduced by two.  In the diagram, the oxidation state of $Fe$ is obtained by counting the number of ionic bonds it has.

And chemistry is more fun than stamp collecting.