Building Tetrahedra

Can you make a tetrahedron whose faces all have the same perimeter?

$n!$ is divisible by $5^3$ so $n!$ must be at least $15$. But $15!$ is only divisible by $2^{11}$ so $n$ is not $15$. $n!$ is not divisible by $17$ so $n$ is less than $17$. Hence $n=16$.