Silicate formulas

You will turn the number of shared corners of a silicate into its oxygen count, its charge and its family, and find how many metal ions balance it.

The idea. A tetrahedron that shares $s$ corners has $4 - s/2$ oxygen atoms of its own. Each oxygen is $2-$ and silicon is $4+$, so the charge for each silicon is $-(4 - s)$.

Your tasks.

1. Complete oxygen_per_silicon(s) so that it returns the oxygen atoms for each silicon.
2. Complete charge_per_silicon(s) so that it returns the charge for each silicon, as a negative number or zero.
3. Complete family(s) so that it returns the name of the family: 0 orthosilicate, 1 pyrosilicate, 2 chain or ring, 2.5 double chain, 3 sheet, 4 framework.
4. Complete cations(s, charge) so that it returns how many metal ions of that charge balance one silicon.