What's up with SiO₂ being tetrahedral?
Every $\boxed{^{14}\textrm{Si}}$ atom is surrounded by 4 $\boxed{^8\textrm{O}}$ atoms.   On the other hand, every $\boxed{^8\textrm{O}}$ atom is surrounded by 2 $\boxed{^{14}\textrm{Si}}$ atoms.   

Suppose that the number of $\textrm{Si-O}$ bonds is $n$, then the number of $\boxed{^{14}\textrm{Si}}$ atoms is $n/4$, while the number of $\boxed{^8\textrm{O}}$ atoms is $n/2$.  Therefore you arrive at the formula $\textrm{Si}\textrm{O}_2$.