Answer
No because $a$ does not increase when the number of faces increases.
Work Step by Step
The formula which gives the edge length $x$ of a polyhedron is:
$$x=\left(\dfrac{V}{a}\right)^{1/3},$$
where $V$ is constant for all polyhedra and $a$ is a constant depending on the polyhedron.
We notice that $a$ increases when the number of faces increases from $4$ to $12$, but then decreases from $12$ to $20$.
Because the values of $a$ do not decrease as the number of faces increases, we cannot conclude that the polyhedron with the greatest number of faces has the smallest edge length.
