We have that
$-2 \sqrt{2} < x < 2 \sqrt{2}$ : $5$ integers
$-2 \sqrt{2} < y < 2 \sqrt{2}$ : $5$ integers
$-2 < z < 2$ : $3$ integers
To find how many non-trivial points $(x, y, z)$ we multiply $5 \cdot 5 \cdot 3$ and substract $1$, which is the case $(0, 0, 0)$, or not??
Then the result is $74$, but in my notes I have that there are $72$ cases... How do we get this result??